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Ardından radyan cinsinden açı hesaplamaları, yayın uzunluğu bulma, yarıçap ve çap hesaplamaları örneklerle anlatılıyor. İkinci bölümde ise çemberde merkez açı, yayın uzunluğu ve yarıçap arasındaki ilişkiler, Türkiye'nin dünya merkezine göre açılarının hesaplanması ve bir tekerlek döndürme animasyonu ile pi sayısı ve radyan kavramı görselleştiriliyor.","Video boyunca çeşitli örnekler ve animasyonlar kullanılarak konu pekiştiriliyor, radyan ve derece arasındaki dönüşümler, pi değerinin 180 dereceye eşit olduğu ve bunun radyan cinsinden nasıl hesaplanacağı gösteriliyor."]},"endTime":781,"title":"Radyan Kavramı ve Çember Problemleri Matematik Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Radyan Kavramı","list":{"type":"unordered","items":["Radyan, bir çemberde yarıçap uzunluğundaki yayı gören merkez açıdır.","Yarıçapı bir metre olan bir çemberde bir metrelik bir yayı gören merkez açı bir radyandır.","Yayın uzunluğu yarıçapa bölünerek radyan değeri 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Kuzey Kampüs & North Campus — Matematik ve Calculus Dünyasına Hoş geldiniz! Detaylı konu anlatımları, kapsamlı soru çözümleri ve sınavlara hazırlık içerikleri burada. Kanalları takip etmeyi...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3830731/36b086d781aa664da00e0c11edaca27c/564x318_1"},"target":"_self","position":"1","reqid":"1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3D4iEdZo9zq40","linkTemplate":"/video/preview/2516890876418832118?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":" 14 | Derece ve Radyan (Degrees & Radians) | Calculus Altın Rehber – Temel Tanım ve Özellikler","related_orig_text":"Radyan","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"Radyan\",\"url\":\"http:\\/\\/www.youtube.com\\/watch?v=4iEdZo9zq40\",\"src\":\"serp\",\"rvb\":\"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_E5MBggQkAYAEKyqLARABGniB__wF-gT8AAP0-gkHCfsC6goQAfv-_gDt9xEFBwEAAPr5C_kCAAAAAgIN8QMAAADq_PsN9gEAABn3-_nzAAAAAvoJBPcAAAD3EO4B_wEAAAj_-AAD_wAACgsOCgAAAAAHEAAP_gAAAAQE_AcAAAAA9u7v_AAAAAAgAC2L-8c7OBNACUhOUAIqcxAAGmA3-QBeJfTJxOUE2voEIQ3w2d8S2J4F_-7NALAW6PrqRbzB6Av_Vfz1BJwAAAAU-OwRJwAkf8vQyAf9PgQNpuEhB1cZBRLI_QLz4bAu9AL-S-0kOxcAuOXe1gyczTcPP9wgAC0gjhY7OBNACUhvUAIqrwYQDBqgBgAAqEEAAABAAAA8QgAAgEEAAEjCAAAwwQAAgEAAAIBAAADwQQAAsMEAACBCAAAAwAAAQMAAAGDCAABgQQAAnsIAAERCAAAQwQAAcMEAAHBCAACqQgAARMIAACDCAADAQAAAIEIAANjBAAAAwgAAwEAAAIDAAAB4QgAAoEEAAOBBAADowQAAVEIAAIA_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-AABEvgAAPD4AADw-AAAEvgAAzr4AAPi9AADoPQAAZL4AAKg9AADePgAAFD4AAHy-AAAcPgAAFD4AADC9AAC6PgAAwj4AAH8_AADIvQAAqD0AAEA8AACgvAAAmL0AALg9AAAwvQAAhj4AAFw-AAAQvQAApr4AAII-AABwvQAAqL0AAEy-AAA0vgAAHL4AAFy-AAAEvgAA4DwAAJo-AAADPwAAgr4AALi9AABAvAAALD4AAHC9AAAsPgAAUL0AAPg9AACIvQAAqD0AAEA8AAAMvgAAQLwAAOY-AACgPAAAoLwAAO4-AAC4vQAADL4AAEC8AAAwvSAAOBNACUh8UAEqjwIQARqAAgAAgDsAAAQ-AACoPQAAa78AAFC9AAAsPgAAij4AAKi9AAB0vgAALD4AAOg9AAAkvgAARL4AADS-AACAuwAAML0AAHS-AAAdPwAA-L0AADw-AADYPQAAuL0AAFC9AAD4vQAAHL4AAGS-AABcvgAAqD0AAIC7AACgvAAA6D0AAFA9AAB0vgAATL4AAIi9AADgvAAAHD4AALg9AADCvgAARL4AAHC9AADgPAAAgDsAAJg9AAAQPQAAPD4AAH-_AAAMPgAA2j4AAKg9AABQPQAAcD0AAEQ-AAC4PQAAqL0AAIg9AACAOwAAcD0AAEQ-AAC4vQAABD4AAKg9AAAcPgAAoDwgADgTQAlIfFABMAk4AUoAYABoAA,,\"}","related_url":"http://www.youtube.com/watch?v=4iEdZo9zq40","parent-reqid":"1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL","related_vfp":1,"relatedVideo":"yes"},"cwidth":1280,"cheight":720,"cratio":1.77777,"dups":["2516890876418832118"],"episode":0,"season":0,"isEmbedOnly":false,"greenHost":"YouTube","hasTranslation":true,"contentTypeId":null,"censored":false},"14201461032485368379":{"videoId":"14201461032485368379","docid":"34-7-5-ZBB9B18B98DD65728","description":"Radyan ↔ Derece dönüşümünü artık ezberlemeye gerek yok! Bu kısa ve öğretici videoda: Derece ↔ Radyan formülünü adım adım öğreniyorsun: Derece → Radyan: derece × π / 180 Radyan → Derece: radyan ×...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2808446/6e04cb3fae0f4fd489950d7214fd600b/564x318_1"},"target":"_self","position":"2","reqid":"1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DceHdQ4q2blw","linkTemplate":"/video/preview/14201461032485368379?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Radyan neden tam anlaşılmıyor? 2 dk da hemen anla: Radyan Nedir, radyan derece dönüşümü #yks #ayt","related_orig_text":"Radyan","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"Radyan\",\"url\":\"http:\\/\\/www.youtube.com\\/watch?v=ceHdQ4q2blw\",\"src\":\"serp\",\"rvb\":\"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_E3GCBCQBgAQrKosBEAEaeIH_BPsB_gIA_gDuCP8H_QLj_BUB_QEBAPb_CgAHAv8A7QQI8gAAAAD9BQgJ-QAAAPb--wj0_wEACvYAAfoAAAAH-Qb59AAAAPgG-QD-AQAAB_8B8wIAAAALBPgFAAAAAAYTBgL-AAAACwT3BAAAAAD44vv8AQAAACAALRPz2Ts4E0AJSE5QAipzEAAaYPb_AGTwEPGs28zT9QAE8fvI3g0Bssv_9-wA3DO8zwTs49P7_f88B-wGqwAAABcZ4xtDAP9q6grCPwBOBOjW-yUVfxQVCcvpOcfewBgHHfgaAFQr3QD66O3VAtz0NBoVNSAALUZJJDs4E0AJSG9QAiqvBhAMGqAGAADgQQAAqEEAAARCAADowQAAFMIAAGRCAACIQgAAcMEAAEjCAAAIwgAAAAAAAMhCAADgwQAAiEEAAERCAABIQgAAoEEAANDBAABAQAAA0MEAACRCAAAgQQAA2EEAAJBBAAAwwQAAgMEAACRCAAAQwgAAAMAAAOBBAACIwQAAaEIAALrCAAAAwQAARMIAALjBAAAEQgAAsEEAAIDAAACIQQAAHEIAANBBAAAAQgAA2EEAAIC_AAC4wQAABEIAALhBAADwQQAAMEEAAGzCAAAAwAAAUMEAAIC_AACQwQAAkEIAADTCAABgwQAAjEIAALBBAACAwQAALMIAAADCAABgwgAANEIAAI7CAACoQQAAMMEAABjCAAAkwgAA3kIAABxCAABowgAAREIAANBBAACAwAAAhMIAANjBAAD4QQAAEEIAABDBAAA0QgAAsMEAAEjCAAAMQgAAMEIAAMZCAAAEwgAAgD8AAIBBAADAQAAAEEIAABTCAACGwgAAAEAAAK7CAAC2QgAAgEAAAARCAAA4QgAA-MIAAJDBAAAEQgAAFMIAAJjBAADgwAAA2EEAAAAAAABAwAAAKEIAAHRCAADYQQAAYMIAAGRCAAAAAAAAMMIAAAAAAACAvwAA8MEAAJDCAADowQAALMIAADBBAAAwwQAAjsIAAIDAAADgQAAANMIAAL7CAAAMQgAAQMEAAILCAAAwwgAAQEAAAMDAAAAAQgAAwEEAACRCAADQwQAA0MEAAMBAAAAIQgAAsEEAAOjBAABAQQAA4EEAAIDBAACQQQAAYEEAAABBAAAAwQAAoMAAAOBBAABoQgAAEEIAAJDBAAC-wgAAqMEAAMjCAADYwQAAQEAAACxCAADIwQAAsEEAAKBBAADAwAAAIMIAAABCAAAgQQAAcMEAABRCAACQwQAA4MEAAITCAADYwQAAqMEAABDCAAB4wgAABMIAAKDBAAAQwQAAMMEAAFzCAADgQQAAQEIAABzCAACQwgAAAMAAACBBAAAQQgAA2EEAADRCAAAwQgAA8EEAAOBAAAAwwQAAEEEAADzCAAAIQgAAdMIgADgTQAlIdVABKo8CEAAagAIAAIC7AAAUvgAARD4AAES-AAAsPgAADz8AAEy-AAADvwAAFD4AAKC8AABAvAAAqL0AAJg9AABcPgAAUD0AAKA8AACAuwAA4LwAAII-AADuPgAAfz8AAAS-AADYPQAAPL4AAFy-AABQPQAANL4AADw-AADgPAAApj4AANg9AAAMvgAAED0AAJg9AAAcvgAAgDsAAMi9AADYPQAA4r4AAIA7AAAsPgAA4DwAANg9AACgvAAARL4AAKC8AAB0PgAAyD0AALg9AACGvgAAqL0AAIg9AACmPgAAyD0AAIK-AAAMPgAA_j4AAKC8AACIPQAAwj4AAIi9AACmvgAAoDwAAFw-IAA4E0AJSHxQASqPAhABGoACAAD4vQAAyL0AAJg9AAA_vwAAhj4AAPg9AACWPgAALL4AAAS-AACWPgAAjj4AAIo-AAC4PQAAbL4AAJg9AACYPQAANL4AAE0_AABwPQAAnj4AAEA8AADgvAAAgj4AAGy-AAA8vgAAgj4AALg9AACCPgAAJL4AAPi9AAD4PQAAMD0AAAS-AABkvgAAEL0AAPg9AADYvQAA0j4AADS-AAB8vgAABT8AAAy-AAAEPgAA-L0AAEA8AACAuwAAf78AAMK-AABkPgAADD4AAFC9AABcPgAAPD4AAIA7AADoPQAAED0AAMi9AAD4vQAAgLsAAHy-AAAwPQAAgDsAAKi9AABQPSAAOBNACUh8UAEwCTgBSgBgAGgA\"}","related_url":"http://www.youtube.com/watch?v=ceHdQ4q2blw","parent-reqid":"1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL","related_vfp":1,"relatedVideo":"yes"},"cwidth":405,"cheight":720,"cratio":0.5625,"dups":["14201461032485368379"],"episode":0,"season":0,"isEmbedOnly":false,"greenHost":"YouTube","hasTranslation":false,"contentTypeId":null,"censored":false},"10815956765300614684":{"videoId":"10815956765300614684","docid":"34-8-4-Z19495E0EBEC65395","description":"Daha fazlası için: http://www.khanacademy.org.tr Matematikten sanat tarihine, ekonomiden fen bilimlerine, basit toplamadan diferansiyel denklemlere, ilkokul seviyesinden üniversite seviyesine...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2134897/9ac3479abcebece51bffb86f68321011/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/oFNkIAEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"4","reqid":"1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=videoid:10815956765300614684","teaser":[{"list":{"type":"unordered","items":["Bu video, matematik eğitimi formatında bir ders anlatımıdır. Bir eğitmen, çemberde yay uzunluğu hesaplama konusunu adım adım açıklamaktadır.","Videoda, çemberde merkez açısının radyan cinsinden ölçüsü verildiğinde yay uzunluğunu hesaplama yöntemi anlatılmaktadır. Eğitmen önce değişkenler tanımlayarak (teta, s, r) problemi basitleştirir, ardından radyanın tanımını açıklar ve yay uzunluğu formülünü (s = r × teta) kullanır. Son olarak, verilen yarıçap (6 cm) ve merkez açı (3/2 radyan) değerlerini kullanarak yay uzunluğunu (9 cm) hesaplar."]},"endTime":157,"title":"Çemberde Yay Uzunluğu Hesaplama Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Çemberde Merkez Açı ve Yay Uzunluğu","list":{"type":"unordered","items":["Çemberde GOH merkez açısının ölçüsü 3/2 radyan olarak verilmiştir.","GH yayının uzunluğu sorulmaktadır.","Çemberin yarıçapı 6 cm olarak belirtilmiştir."]},"beginTime":1,"endTime":12,"href":"/video/preview/10815956765300614684?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=1&ask_summarization=1"},{"index":1,"title":"Değişken Tanımlama ve Radyan Tanımı","list":{"type":"unordered","items":["Merkez açıya teta, yay uzunluğuna s, yarıçapa r değişkenleri tanımlanmıştır.","Radyanın tanımı: Bir açının radyan cinsinden ölçüsü, açının karşısındaki yayın uzunluğunun çemberin yarıçapına oranıdır.","Birim çemberde açının ölçüsü yayın uzunluğuna eşittir, ancak her durumda açının ölçüsü yayın uzunluğunun yarıçapa oranıdır."]},"beginTime":12,"endTime":105,"href":"/video/preview/10815956765300614684?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=12&ask_summarization=1"},{"index":2,"title":"Yay Uzunluğu Hesaplama","list":{"type":"unordered","items":["Yay uzunluğu formülü: s = r × teta'dır.","Yarıçap 6 cm, açının radyan ölçüsü 3/2 radyan olduğundan, yay uzunluğu s = 6 cm × 3/2 = 9 cm olarak hesaplanmıştır."]},"beginTime":105,"endTime":151,"href":"/video/preview/10815956765300614684?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=105&ask_summarization=1"}],"linkTemplate":"/video/preview/10815956765300614684?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Örnek: Radyan Ölçüsü ve Yay Uzunluğu (Trigonometri) 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fazlası için: http://www.khanacademy.org.tr Matematikten sanat tarihine, ekonomiden fen bilimlerine, basit toplamadan diferansiyel denklemlere, ilkokul seviyesinden üniversite seviyesine...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3683525/c05e33ae1657f18d85daba772fe8b89c/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/wFUyZAAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"6","reqid":"1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=videoid:1141642780541761015","teaser":[{"list":{"type":"unordered","items":["Bu video, bir eğitmen tarafından sunulan matematik dersidir. Eğitmen, çember çizerek konuyu görsel olarak açıklamaktadır.","Video, derece ve radyan arasındaki ilişkiyi anlatarak başlıyor ve çemberin etrafında bir tur atıldığında 360 derece ve 2π radyan olduğunu gösteriyor. Ardından 150 dereceyi ve -45 dereceyi radyana çevirmek için adım adım hesaplamalar yapılıyor. Eğitmen, her derece için π/180 radyan olduğunu hesaplayarak 150 dereceyi 5π/6 radyana, -45 dereceyi ise -π/4 radyana dönüştürüyor."]},"endTime":255,"title":"Derece ve Radyan Dönüşümleri Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Derece ve Radyan Arasındaki İlişki","list":{"type":"unordered","items":["150 derece ve -45 dereceyi radyana çevirmek gerekiyor.","Çemberin etrafında bir tur dönersek 360 derece yol kat etmiş oluruz.","Çemberin etrafında bir tur attığımızda 2π radyan gitmiş oluruz çünkü yayın uzunluğu çemberin çevresine eşittir."]},"beginTime":1,"endTime":74,"href":"/video/preview/1141642780541761015?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=1&ask_summarization=1"},{"index":1,"title":"Derece ve Radyan Arasındaki Eşitlikler","list":{"type":"unordered","items":["2π radyanlık bir açı ölçüsü 360 dereceye eşittir.","Her π radyan 180 derece veya her derece π/180 radyan eşittir.","Her radyan 180/π 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Video, radyan ve derece birimleri arasındaki temel ilişkiyi ve dönüşüm formülünü öğrenmek isteyenler için faydalı olacaktır."]},"endTime":144,"title":"Radyan ve Derece Dönüşümleri Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Radyan ve Derece Arasındaki Eşleme","list":{"type":"unordered","items":["Bir tam devir (bir tur) 2π radyan ve 360 dereceye eşittir.","2π radyan ve 360 dereceyi her ikisini de 2'ye böldüğümüzde π radyan = 180 derece eşitliği elde edilir.","π radyan, çemberin etrafında yarım tur anlamına gelir."]},"beginTime":0,"endTime":77,"href":"/video/preview/15818732569747867135?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=0&ask_summarization=1"},{"index":1,"title":"Eksi Pi Bölü Üç Radyanı Dereceye Çevirme","list":{"type":"unordered","items":["Eksi π/3 radyanı dereceye çevirmek için önce bir radyanın kaç dereceye eşit olduğunu bulmak gerekir.","180 derecenin π radyan olduğunu biliyoruz, bu nedenle 1 radyan = 180/π dereceye eşittir.","Eksi π/3 radyanı dereceye çevirince -60° sonucuna ulaşılır."]},"beginTime":77,"endTime":136,"href":"/video/preview/15818732569747867135?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=77&ask_summarization=1"}],"linkTemplate":"/video/preview/15818732569747867135?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Radyanı Dereceye Dönüştürme 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fazlası için: http://www.khanacademy.org.tr Matematikten sanat tarihine, ekonomiden fen bilimlerine, basit toplamadan diferansiyel denklemlere, ilkokul seviyesinden üniversite seviyesine...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3924252/3e3f3b104b14c0095695467e4a4c64dc/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/3xK_wwAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"9","reqid":"1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=videoid:7956925663861492515","teaser":[{"list":{"type":"unordered","items":["Bu video, bir eğitim dersi formatında olup, bir eğitmen tarafından radyan ve derece konusu anlatılmaktadır.","Video, radyanın tanımı ve çemberle ilişkisiyle başlayıp, radyan ve derece arasındaki ilişkiyi açıklamaktadır. Eğitmen, bir radyanın r uzunluğundaki yaya karşılık gelen açı olduğunu, çemberin 2π radyan olduğunu ve bu bilgileri kullanarak radyan-derece dönüşüm formüllerini (1 radyan = 180/π derece, 1 derece = π/180 radyan) türetmektedir. Daha sonra bu formülleri kullanarak çeşitli örnekler üzerinden dönüşümleri göstermektedir."]},"endTime":389,"title":"Radyan ve Derece Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Radyan Kavramı","list":{"type":"unordered","items":["Radyan, açı ölçümünde kullanılan bir birimdir ve bir radyan, yarıçap uzunluğundaki yaya karşılık gelen açıdır.","Radyan kelimesi İngilizce \"radius\" (yarıçap) kelimesinden türemiştir.","Çemberin tamamı 360 derece veya 2π radyan olarak ifade edilir."]},"beginTime":0,"endTime":149,"href":"/video/preview/7956925663861492515?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=0&ask_summarization=1"},{"index":1,"title":"Radyan ve Derece Arasındaki İlişki","list":{"type":"unordered","items":["Bir derece, 180/π radyan'a eşittir.","Bir radyan, π/180 dereceye eşittir.","Yarım çember 180 derece veya π radyan olarak ifade edilir."]},"beginTime":149,"endTime":233,"href":"/video/preview/7956925663861492515?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=149&ask_summarization=1"},{"index":2,"title":"Örneklerle Uygulama","list":{"type":"unordered","items":["45 derece, π/4 radyan'a eşittir.","30 derece, π/6 radyan'a eşittir.","Radyan ve derece, açı ölçümünde kullanılan iki farklı birimdir, günlük hayatta derece daha yaygın kullanılır."]},"beginTime":233,"endTime":384,"href":"/video/preview/7956925663861492515?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=233&ask_summarization=1"}],"linkTemplate":"/video/preview/7956925663861492515?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Radyan ve Derece 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Eğitmen, radyan kavramını ve derece ile radyan arasındaki dönüşümleri açıklamaktadır.","Video, radyanın tanımıyla başlayıp, yarıçap uzunluğundaki bir yayı gören merkez açının ölçüsünün bir radyan olduğunu göstermektedir. Eğitmen, 180 derecenin aslında π radyan olduğunu, 1 radyanın yaklaşık 57,29 derece olduğunu ve derece-dakika-saniye cinsinden nasıl ifade edilebileceğini açıklamaktadır. Ayrıca, derece ile radyan arasında dönüşüm yapmak için kullanılan formülleri (π/180) detaylı olarak anlatmaktadır. Video, 11. sınıf yönlü açılar konusuna da atıfta bulunarak, daha detaylı bilgi için ilgili videolara yönlendirmektedir."]},"endTime":470,"title":"Radyan Kavramı ve Dönüşümleri","beginTime":0}],"fullResult":[{"index":0,"title":"Radyanın Tanımı","list":{"type":"unordered","items":["Radyan, yarıçap uzunluğundaki bir yayı gören merkez açının ölçüsüdür.","Bir çemberin yarıçapı r ise, r kadar uzunluğundaki bir yayı gören açının ölçüsü bir radyandır.","İki r uzunluğunda bir yayı gören açının ölçüsü iki radyan, üç r uzunluğunda bir yayı gören açının ölçüsü üç radyandır."]},"beginTime":0,"endTime":100,"href":"/video/preview/5262966383472159213?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=0&ask_summarization=1"},{"index":1,"title":"Pi Sayısı ve Radyan İlişkisi","list":{"type":"unordered","items":["180 derece, pi radyan olarak ifade edilir, ancak genellikle \"pi derece\" şeklinde söylenir.","Yarım çember 180 derece (π radyan), tam çember ise 360 derece (2π radyan) olarak ifade edilir.","Bir radyan yaklaşık olarak 57,29 dereceye tekabül eder ve derece-dakika-saniye olarak 57 derece 17 dakika 45 saniyeye denk gelir."]},"beginTime":100,"endTime":314,"href":"/video/preview/5262966383472159213?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=100&ask_summarization=1"},{"index":2,"title":"Dönüşümler","list":{"type":"unordered","items":["Derece ile pi radyan arasında dönüşüm yapmak için oran orantı kullanılır.","Derece olarak açı, radyan olarak açıya eşittir (derece × π / 180).","Radyan olarak açı, derece olarak açıya eşittir (radyan / derece × π / 180)."]},"beginTime":314,"endTime":469,"href":"/video/preview/5262966383472159213?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=314&ask_summarization=1"}],"linkTemplate":"/video/preview/5262966383472159213?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Radyan | pi radyan kaç derece | π sayısı | 180° | 3,14 | pi sayısı 180 derece mi | pi radyan 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fazlası için: http://www.khanacademy.org.tr Matematikten sanat tarihine, ekonomiden fen bilimlerine, basit toplamadan diferansiyel denklemlere, ilkokul seviyesinden üniversite seviyesine...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3047125/3c0b6661fab7b1653eb48de09b73d651/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/uNTKIgEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"11","reqid":"1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=videoid:1039435321843030914","teaser":[{"list":{"type":"unordered","items":["Bu video, bir eğitim dersi formatında radyan ve derece birimleri arasındaki dönüşümleri anlatan bir içeriktir.","Video, radyan ve derece arasındaki temel ilişkiyi (çemberin bir tur dönmesi 2π radyan, 360 derece) hatırlatarak başlıyor. Ardından 1 radyan = 180/π derece ve 1 derece = π/180 radyan formüllerini açıklıyor. Daha sonra 30 derece → radyan, π/3 radyan → derece, 45 derece → radyan ve -π/2 radyan → derece gibi çeşitli örnekler üzerinden dönüşüm işlemlerini adım adım gösteriyor. Video, bu tür alıştırmaların tekrarlanmasının önemini vurgulayarak sona eriyor."]},"endTime":337,"title":"Radyan ve Derece Arasındaki Dönüşüm Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Radyan ve Derece Arasındaki Bağıntı","list":{"type":"unordered","items":["Çemberin bir tam tur dönmesi 2π radyana eşittir ve bu 360 dereceye denk gelir.","π radyan 180 dereceye eşittir, yani çemberin etrafında yarım tur dönersek π radyan olur.","1 radyan 180/π dereceye eşittir ve 1 derece π/180 radyana eşittir."]},"beginTime":0,"endTime":74,"href":"/video/preview/1039435321843030914?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=0&ask_summarization=1"},{"index":1,"title":"Dereceyi Radyana Çevirme Örneği","list":{"type":"unordered","items":["30 dereceyi radyana çevirmek için 30 derece × (π/180 derece) formülü kullanılır.","Sadeleştirme sonucunda 30 derece = π/6 radyan olarak bulunur."]},"beginTime":74,"endTime":154,"href":"/video/preview/1039435321843030914?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=74&ask_summarization=1"},{"index":2,"title":"Radyanı Dereceye Çevirme Örneği","list":{"type":"unordered","items":["π/3 radyanı dereceye çevirmek için 180/π formülü kullanılır.","Sadeleştirme sonucunda π/3 radyan = 60 derece olarak bulunur."]},"beginTime":154,"endTime":202,"href":"/video/preview/1039435321843030914?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=154&ask_summarization=1"},{"index":3,"title":"Diğer Örnekler","list":{"type":"unordered","items":["45 derece = π/4 radyan olarak çevrilir.","Negatif π/2 radyan = -90 derece olarak çevrilir.","Daha fazla örnek çözersek zamanla daha hızlı ve içgüdüsel olarak cevap bulabiliriz."]},"beginTime":202,"endTime":326,"href":"/video/preview/1039435321843030914?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=202&ask_summarization=1"}],"linkTemplate":"/video/preview/1039435321843030914?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Radyan ve Derece 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fazlası için: http://www.khanacademy.org.tr Matematikten sanat tarihine, ekonomiden fen bilimlerine, basit toplamadan diferansiyel denklemlere, ilkokul seviyesinden üniversite seviyesine...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3382046/a47c49fe4580a04d14b6f950db059f9d/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/O3r-JQAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"13","reqid":"1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=videoid:11112349055128620047","teaser":[{"list":{"type":"unordered","items":["Bu video, matematik eğitimi formatında bir ders anlatımıdır. Eğitmen, açıların ölçülmesi konusunu detaylı bir şekilde açıklamaktadır.","Video, önce derece kavramını ve 360 derecenin neden bu kadar önemli olduğunu açıklayarak başlıyor. Ardından radyan kavramını tanımlıyor ve bir çemberde bir radyanlık açının ölçüsünün çemberin yarıçapına eşit olduğunu gösteriyor. Son olarak, derece ve radyan arasındaki dönüşümleri (2π radyan = 360 derece ve π radyan = 180 derece) matematiksel olarak açıklıyor. Video, bu dönüşümleri pratik uygulamalarla pekiştireceğini belirterek sona eriyor."]},"endTime":450,"title":"Açının Ölçüsü: Derece ve Radyan","beginTime":0}],"fullResult":[{"index":0,"title":"Derece Ölçüsü","list":{"type":"unordered","items":["Derece, insanların yarattığı bir kavramdır ve açı ölçüsü için kullanılan temel birimdir.","360 derece, bir tam tur anlamına gelir ve bu değer eski takvimlerde bir sene 360 gün olduğu ve gök cisimlerinin her gün 360'lık bir mesafe kat ettiği gözlemlerinden gelmektedir.","Babilliler 60 tabanlı bir sayı sistemi kullanıyorlardı ve bir çemberin içine altı tane ikizkenar üçgen koyduğunuzda, her üçgen 60 tabanında 60 kesiti ayırdığınızda 360 derece elde edersiniz."]},"beginTime":0,"endTime":138,"href":"/video/preview/11112349055128620047?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=0&ask_summarization=1"},{"index":1,"title":"Radyan Ölçüsü","list":{"type":"unordered","items":["Radyan, bir çemberde bir radyanlık açıya karşılık gelen yayın uzunluğunun çemberin yarıçapına eşit olduğu bir ölçü birimidir.","Yarıçap uzunluğundaki yayı gören açının ölçüsü bir radyandır ve bu tanım çember konusunu işlerken çok işimize yarar.","Bir çemberin çevresi 2πr olduğundan, tam bir tur dönen açının ölçüsü 2π radyandır."]},"beginTime":138,"endTime":317,"href":"/video/preview/11112349055128620047?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=138&ask_summarization=1"},{"index":2,"title":"Derece ve Radyan Arasındaki Dönüşüm","list":{"type":"unordered","items":["2π radyan 360 dereceye eşittir, bu nedenle π radyan 180 dereceye eşittir.","1 radyan 180/π dereceye eşittir.","1 derece π/180 radyana 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kanala destek için abone olamyı unutmayalım. Açıklama: Neden pi sayısı 3.14 gibi bir değer iken trigonometride 180 derece olarak alınıyor? İki değer arasındaki ilişki nereden geliyor?","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/1535112/56d19cac450dd32484f1aff68fa2df3b/564x318_1"},"target":"_self","position":"14","reqid":"1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3D2W4HXa-Sxpw","linkTemplate":"/video/preview/7924905973026902559?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"pi sayısı ile radyan ilişkisi, radyan 3.14 mü ? 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fazlası için: http://www.khanacademy.org.tr Matematikten sanat tarihine, ekonomiden fen bilimlerine, basit toplamadan diferansiyel denklemlere, ilkokul seviyesinden üniversite seviyesine...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3132080/f7b88da039a08eab4b1620291bb7ae1a/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/8dTFMwAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"15","reqid":"1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=videoid:6031144218490336692","teaser":[{"list":{"type":"unordered","items":["Bu video, matematik eğitimi formatında bir ders anlatımıdır. Eğitmen, radyan cinsinden verilen açı ölçülerinin grafik üzerinde nasıl gösterileceğini açıklamaktadır.","Videoda, açının köşesinin orijin üzerinde ve kenarlarından birinin x ekseni üzerinde olduğu varsayımı yapılarak, pembe ışınla başlayıp saat yönünün tersine dönerek üç farklı açı ölçüsü (3π/5, 2π/7 ve 3π) elde edilmektedir. Eğitmen, bu açıların hangi bölgede olduğunu belirlemek için pi/2 ve pi değerlerini kullanarak karşılaştırma yapmakta ve grafik üzerinde göstermektedir. Video, izleyicilere önce kendi başlarına denemelerini, sonra da eğitmenin adım adım çözümünü göstermektedir."]},"endTime":238,"title":"Radyan Cinsinden Açı Ölçüleri ve Grafik Üzerindeki Gösterimi","beginTime":0}],"fullResult":[{"index":0,"title":"Radyan Cinsinden Açı Ölçüleri","list":{"type":"unordered","items":["Bu videoda radyan cinsinden verilen açı ölçülerinin grafik üzerinde nasıl gösterildiği anlatılacak.","Açıların daha kolay gösterilmesi için açının köşesinin orijin üzerinde ve bir kenarının x ekseni üzerinde olduğunu varsayacağız.","Pembe ışını orijin etrafında saat yönünün tersine döndürerek farklı açı ölçüleri elde edilecek ve hangi bölgelere düştükleri saptanacak."]},"beginTime":0,"endTime":69,"href":"/video/preview/6031144218490336692?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=0&ask_summarization=1"},{"index":1,"title":"Üç Pi Bölü Beş Radyan","list":{"type":"unordered","items":["Üç pi bölü beş radyan, pi bölü iki (90 derece) radyandan büyüktür.","Üç pi bölü beş radyan, pi (180 derece) radyandan küçüktür.","Üç pi bölü beş radyanlık açı ikinci bölgede gösterilir."]},"beginTime":69,"endTime":157,"href":"/video/preview/6031144218490336692?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=69&ask_summarization=1"},{"index":2,"title":"İki Pi Bölü Yedi Radyan","list":{"type":"unordered","items":["İki pi bölü yedi radyan, pi bölü iki (90 derece) radyandan küçüktür.","İki pi bölü yedi radyan, pi bölü iki radyandan büyük ve birinci bölgede gösterilir."]},"beginTime":157,"endTime":195,"href":"/video/preview/6031144218490336692?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=157&ask_summarization=1"},{"index":3,"title":"Üç Radyan","list":{"type":"unordered","items":["Üç radyan, pi (180 derece) radyandan biraz küçüktür.","Üç radyan, pi bölü iki (90 derece) radyandan büyüktür.","Üç radyanlık açı da ikinci bölgede gösterilir."]},"beginTime":195,"endTime":224,"href":"/video/preview/6031144218490336692?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=195&ask_summarization=1"}],"linkTemplate":"/video/preview/6031144218490336692?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Radyan Cinsinden Açılar ve Koordinat Sisteminde Bölgeler 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çok kullanılan açı birimi olan \"Radyan\" birimini anlattığım video. Kuru kuru ezberleyerek değil, mantığını kavrayarak, bilgiler arasında bağlantı kurarak öğrenin...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2799703/cd3cb1abf1b2f492691239906b240f25/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/wAtIeQEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"16","reqid":"1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=videoid:5785282610166947950","teaser":[{"list":{"type":"unordered","items":["Bu video, \"Matematik Sevdiren Hoca\" kanalında yayınlanan bir matematik dersidir. Eğitmen, radyan kavramını anlatmaktadır.","Videoda radyan kavramı detaylı olarak açıklanmaktadır. Önce çemberin çevre uzunluğu ve yay uzunluğu arasındaki ilişki anlatılmakta, ardından bir radyanın tanımı verilmektedir. Bir radyan, çemberin yarıçapı uzunluğundaki yayın üzerinde yol alındığında oluşan açıdır. Son olarak, bir çemberin çevresinin 2π radyan olduğunu ve bunun neden böyle olduğunu matematiksel olarak açıklamaktadır."]},"endTime":410,"title":"Radyan Kavramı Matematik Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Çemberin Çevre Uzunluğu ve Yay Sayısı","list":{"type":"unordered","items":["Yarıçapı r olan bir çemberin çevre uzunluğu 2πr'dir.","Çemberin çevresini bir yay uzunluğuna böldüğümüzde yay sayısını bulabiliriz.","Örneğin, çevresi 16 birim olan bir çemberde 2 birimlik yay sayısı 16/2=8'dir."]},"beginTime":23,"endTime":136,"href":"/video/preview/5785282610166947950?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=23&ask_summarization=1"},{"index":1,"title":"Radyan Kavramı","list":{"type":"unordered","items":["Bir radyan, yarıçap uzunluğundaki yayı gören açıdır.","Çemberin çevresi 2πr birimdir ve bu çevre 2π radyanlık bir açı oluşturur.","Bir çemberin çevresinin 2π radyan olduğunu, bir radyanın yarıçap uzunluğundaki yayı gören açı olduğunu ve yay sayısının çevre bölü bir yay uzunluğu olduğunu öğrendik."]},"beginTime":136,"endTime":406,"href":"/video/preview/5785282610166947950?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=136&ask_summarization=1"}],"linkTemplate":"/video/preview/5785282610166947950?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Trigonometri-3 ( Radyan Nedir ? 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Eğitmen, trigonometri konusunu öğrencilere anlatmaktadır.","Video, trigonometri konusunun zorluğunu ele alarak başlıyor ve derece, dakika ve saniye arasındaki dönüşümleri örneklerle açıklıyor. Ardından derece ve radyan arasındaki ilişki birim çember üzerinden anlatılıyor ve dönüşüm formülü (derece/180 = radyan/π) açıklanıyor. Ayrıca açıların esas ölçülerini bulma yöntemleri ve üçgenlerde açı hesaplamaları detaylı olarak ele alınıyor.","Video, trigonometri konusunu başlık başlık inceleyerek öğrencilere konuyu daha kolay anlamaları için yardımcı olmayı amaçlıyor ve bir sonraki bölümde devam edeceğini belirterek sona eriyor."]},"endTime":1472,"title":"Trigonometri Dersi: Derece ve Radyan Dönüşümleri","beginTime":0}],"fullResult":[{"index":0,"title":"Trigonometri Konusuna Giriş","list":{"type":"unordered","items":["Trigonometri, öğrencilerin zorlandığı ve gözünde büyüttüğü bir konudur.","Bu konuyu aşama aşamak başlık başlık hallederseniz rahatlıkla üstesinden gelebilirsiniz.","Trigonometride geometri bilgisi de önemlidir çünkü şekilli sorular vardır."]},"beginTime":1,"endTime":34,"href":"/video/preview/4515583101402280641?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=1&ask_summarization=1"},{"index":1,"title":"Derece, Dakika ve Saniye Dönüşümleri","list":{"type":"unordered","items":["Bir derecelik açı altmış dakika, bir dakika ise altmış saniyedir.","Dereceyi saniyeye çevirmek için 3600 ile çarpılır.","Saniyeyi dakikaya çevirmek için 60'a bölünür, dakikayı dereceye çevirmek için tekrar 60'a bölünür."]},"beginTime":34,"endTime":252,"href":"/video/preview/4515583101402280641?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=34&ask_summarization=1"},{"index":2,"title":"Açı Toplama ve Çıkarma İşlemleri","list":{"type":"unordered","items":["Açıları toplarken saniye ve dakika 60'dan büyükse, onların 60'ı yarın tarafa bir olarak aktarılır.","Üçgen iç açıları toplamı 180 derecedir.","Açılarda çıkarma işlemi yaparken, 180 derecenin dakikası ve saniyesi olduğu için bir dereceye aktarılır."]},"beginTime":252,"endTime":654,"href":"/video/preview/4515583101402280641?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=252&ask_summarization=1"},{"index":3,"title":"Derece ve Radyan Arasındaki İlişki","list":{"type":"unordered","items":["Birim çemberde saat yönünün tersine gidersek açı pozitif, saat yönünde gidersek açı negatif olur.","Bir tur atınca derece olarak 360 derece, radyan olarak 2π döner.","Trigonometride π'nin 180 dereceye eşit olduğu kabul edilir ve dönüşüm yaparken \"derece/180 = radyan/π\" formülü kullanılır."]},"beginTime":654,"endTime":782,"href":"/video/preview/4515583101402280641?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=654&ask_summarization=1"},{"index":4,"title":"Üçgen Açıları ve Radyan Dönüşümü","list":{"type":"unordered","items":["Üçgenin iç açıları toplamı 180 derecedir, bu bilgi kullanılarak verilen açılarla üçüncü açı bulunabilir.","Dereceyi radyana çevirmek için 180 dereceyi π ile çarpıp, açının derecesini 180'e bölerek sadeleştirme yapılır.","Radyanı dereceye çevirmek için π yerine 180 yazılır ve açı değeri 180'e bölünür."]},"beginTime":785,"endTime":979,"href":"/video/preview/4515583101402280641?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=785&ask_summarization=1"},{"index":5,"title":"Esas Ölçü Kavramı","list":{"type":"unordered","items":["Esas ölçü, bir açının pozitif yönde bir tur attıktan sonra kalan açıdır.","Derecede esas ölçü bulunurken açı 360'a bölünür ve kalan alınır, negatif açılar için 360'dan çıkarılır.","Radyanda esas ölçü bulunurken tek sayılarda π, çift sayılarda 0 derece alınır, kesirli radyanlarda paydanın iki katına bölünür ve kalan alınır."]},"beginTime":979,"endTime":1142,"href":"/video/preview/4515583101402280641?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=979&ask_summarization=1"},{"index":6,"title":"Esas Ölçü Örnekleri","list":{"type":"unordered","items":["4153 derecenin esas ölçüsü 193 derecedir, 11 tur attıktan sonra kalan açıdır.","-1685 derecenin esas ölçüsü 115 derecedir, negatif açılar için 360 dereceden çıkarılır.","87π/7 radyanın esas ölçüsü 3π/7, -143/5 radyanın esas ölçüsü 7π/5'tir."]},"beginTime":1142,"endTime":1350,"href":"/video/preview/4515583101402280641?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=1142&ask_summarization=1"},{"index":7,"title":"Üçgende Esas Ölçü Uygulaması","list":{"type":"unordered","items":["ABC üçgeninde A ve B açıları sırasıyla -71/4 ve 91/3 radyanlık açıların esas ölçülerine eşittir.","A açısının esas ölçüsü 45 derece, B açısının esas ölçüsü 60 derece olarak bulunur.","Üçgenin C açısının ölçüsü 75 derecedir, A ve B açılarının toplamı 105 derece olduğundan 180 dereceden çıkarılarak hesaplanır."]},"beginTime":1350,"endTime":1470,"href":"/video/preview/4515583101402280641?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=1350&ask_summarization=1"}],"linkTemplate":"/video/preview/4515583101402280641?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Trigonometriye Giriş Derece, Dakika, Saniye, Radyan Ve Bir Açının Esas 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Matematik ► Trigonometri 🔗 Bu dersimizde derece ve radyan kavramlarını tanıyıp, dereceden radyana ve radyandan dereceye geçiş formülü üzerine sorular...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/214617/ac9b9a1e30e192453c3fd2f4762d423b/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/O9FARwEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"18","reqid":"1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=videoid:13342010549221050348","teaser":[{"list":{"type":"unordered","items":["Bu video, bir öğretmen/eğitmen tarafından sunulan eğitim içeriğidir.","Video, trigonometri konusunun üçüncü başlığı olan derece ile radyan dönüşümleri ile başlayıp, çemberde merkez açı ve yay uzunluğu hesaplamaları konularını kapsamaktadır. İlk bölümde derece ve radyan kavramları tanımlanarak dönüşüm formülleri (d = 180r/π ve r = πd/180) açıklanırken, ikinci bölümde çemberde merkez açı hesaplamaları için iki farklı yöntem gösterilmektedir.","Videoda teorik bilgilerin yanı sıra pratik örnekler de yer almaktadır. Özellikle yarıçap ve yayın uzunluğu verilen durumlarda merkez açı hesaplamaları hem derece hem de radyan cinsinden yapılmaktadır. Video, bir sonraki derste birim çember konusuna geçileceği bilgisiyle sonlanmaktadır."]},"endTime":799,"title":"Trigonometri: Derece ile Radyan Dönüşümleri ve Çemberde Açı Hesaplamaları","beginTime":0}],"fullResult":[{"index":0,"title":"Derece ve Radyan Kavramları","list":{"type":"unordered","items":["Bu videoda trigonometri konusunda derece ile radyan dönüşümleri incelenecektir.","Bir tam çemberin çevresinin 360 eş parçasından birini gören merkez açının ölçüsüne bir derece denir.","Bir tam çemberin yarıçap uzunluğuna eşit uzunluktaki yayı gören merkez açının ölçüsüne bir radyan denir."]},"beginTime":2,"endTime":85,"href":"/video/preview/13342010549221050348?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=2&ask_summarization=1"},{"index":1,"title":"Derece ve Radyan Arasındaki İlişki","list":{"type":"unordered","items":["Bir radyan yaklaşık olarak 57,30 dereceye tekabül eder.","Pi radyan yaklaşık olarak 180 dereceye eşittir.","Trigonometride pi 180 derece olarak alınmaz, pi her yerde 3,14'tür; 180 derece olan pi radyandır."]},"beginTime":85,"endTime":243,"href":"/video/preview/13342010549221050348?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=85&ask_summarization=1"},{"index":2,"title":"Dönüşüm Formülleri","list":{"type":"unordered","items":["Derece ve radyan arasındaki dönüşümlerde d/180 = r/π formülü kullanılır.","Dereceden radyana geçerken formül kullanmak faydalı olurken, radyandan dereceye geçerken π yerine 180 derece yazarak formüle girmeden çözüm yapılabilir.","Karmaşık örneklerde π yerine 180 derece yazarak tüm denklemleri derece cinsine dönüştürmek mümkündür."]},"beginTime":243,"endTime":433,"href":"/video/preview/13342010549221050348?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=243&ask_summarization=1"},{"index":3,"title":"Örnekler","list":{"type":"unordered","items":["İlk örnekte verilen eşitliklerde π yerine 180 derece yazarak denklemler çözülür ve x-y farkı bulunur.","İkinci örnekte π/3 radyan açısı derece, dakika ve saniye cinsine çevrilir.","Üçüncü örnekte yarıçapı 18 cm olan bir çemberde 15π cm uzunluğundaki yayı gören merkez açının ölçüsü sorulur."]},"beginTime":433,"endTime":595,"href":"/video/preview/13342010549221050348?parent-reqid=1769499974786350-17545995235081671659-balancer-l7leveler-kubr-yp-vla-100-BAL&text=Radyan&t=433&ask_summarization=1"},{"index":4,"title":"Merkez Açı ve Yay Uzunluğu İlişkisi","list":{"type":"unordered","items":["Yarıçapı 18 santim olan bir çemberin çevresi 36π santimdir ve bu çevre 360 derecelik açıyı görür.","15π santim uzunluğundaki yayı gören merkez açı, oran orantı ile 150 derece olarak bulunur.","Açı küçüldükçe gördüğü yay da küçülür, bu nedenle açı ve yay uzunluğu arasında doğru orantı 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