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Eğitmen, trigonometride kullanılan açı birimleri hakkında bilgi vermektedir.","Video, trigonometride derece yerine radyan biriminin neden tercih edildiğini açıklamaktadır. Eğitmen, birim çember üzerinde radyan kavramını anlatarak, bir dairenin çevresinin yarıçapıyla değiştiğini ve birim çemberin çevresinin 2π olduğunu açıklar. Ardından derece-radyan dönüşümleri için formülleri (π = 180°) ve önemli açıların radyan değerlerini (π/4, π/6, π/3, π/2, π) birim çember üzerinde göstererek anlatır. Video, trigonometride radyan kavramının temel prensiplerini ve pratik kullanımını içermektedir."]},"endTime":490,"title":"Trigonometride Radyan Kavramı ve Derece-Radyan Dönüşümleri","beginTime":0}],"fullResult":[{"index":0,"title":"Trigonometride Radyan Ölçüsü","list":{"type":"unordered","items":["Trigonometride derece yerine radyan birimi kullanılır çünkü derece gelişigüzel seçilmiş bir birimdir.","Birim çemberde yarıçapı bir olan çemberde, açı ölçümü yay uzunluğuyla yapılır.","Birim çemberin çevresi 2π'dir ve bu tam bir dönüşe (360 derece) denk gelir."]},"beginTime":0,"endTime":104,"href":"/video/preview/7315710117323179139?parent-reqid=1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-BAL&text=Radyan+Design&t=0&ask_summarization=1"},{"index":1,"title":"Radyan ve Derece Arasındaki İlişki","list":{"type":"unordered","items":["Tam dönüş 2π, yarım dönüş π, çeyrek dönüş π/2 radyandır.","Birim çemberin yarı çemberi π uzunluğundadır ve yaklaşık 3,14 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Radyan nasıl hesaplanır? Konu anlatımı Soru çözümleri Radyan türünden esas ölçü...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/4566067/9253b4e1e2f1bbdb89b4e28c1699ace2/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/bXsJGwIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"10","reqid":"1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-BAL&text=videoid:8008296315112459252","teaser":[{"list":{"type":"unordered","items":["Bu video, bir eğitmen tarafından sunulan matematik eğitim içeriğidir.","Video, radyan kavramının tanımı ve özellikleri ile başlayıp, yarıçap uzunluğundaki yayı gören merkez açının bir radyan olduğunu açıklıyor. 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 bulunur."]},"beginTime":0,"endTime":36,"href":"/video/preview/8008296315112459252?parent-reqid=1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-BAL&text=Radyan+Design&t=0&ask_summarization=1"},{"index":1,"title":"Radyan Örnekleri","list":{"type":"unordered","items":["Yarıçapı bir metre olan bir çemberde iki metrelik bir yayı gören merkez açı iki radyandır.","Yarıçapı bir metre olan bir çemberde üç metrelik bir yayı gören merkez açı üç radyandır.","Yarıçapı iki metre olan bir çemberde iki metrelik bir yayı gören merkez açı bir radyandır.","Yarıçapı üç metre olan bir çemberde birvirgülelli metrelik bir yayı gören merkez açı buçuk radyandır.","Yarıçapı dört metre olan bir çemberde yirmi metrelik yayı gören merkez açı beş radyandır."]},"beginTime":36,"endTime":103,"href":"/video/preview/8008296315112459252?parent-reqid=1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-BAL&text=Radyan+Design&t=36&ask_summarization=1"},{"index":2,"title":"Radyan Problemleri","list":{"type":"unordered","items":["Yarıçapı sekiz metre olan bir çemberde birvirgülotuz radyanlık bir merkez açının gördüğü yayın uzunluğu onvirgülkırk metredir.","Yarıçapı oniki metre olan bir çemberde yirmibir metrelik bir yayı gören merkez açının radyan değeri birvirgülyetmişbeş radyandır.","Bir çemberde yirmiyedi metrelik bir yayı gören merkez açı birvirgülseksen radyan olduğuna göre çemberin çapı otuz metredir."]},"beginTime":103,"endTime":209,"href":"/video/preview/8008296315112459252?parent-reqid=1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-BAL&text=Radyan+Design&t=103&ask_summarization=1"},{"index":3,"title":"Radyan ve Derece İlişkisi","list":{"type":"unordered","items":["Merkez açının tamamı iki pi radyandır ve üçyüzaltmış dereceye eşittir.","Çemberin çevresi iki pi r olduğundan, yayın uzunluğu yarıçapa bölündüğünde iki pi elde edilir.","Pi yerine yüzseksen derece yazarak radyan ve derece arasındaki ilişkiyi bulabiliriz."]},"beginTime":209,"endTime":294,"href":"/video/preview/8008296315112459252?parent-reqid=1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-BAL&text=Radyan+Design&t=209&ask_summarization=1"},{"index":4,"title":"Radyan ve Derece Dönüşümleri","list":{"type":"unordered","items":["İki pi radyan, üçyüzaltmış dereceye eşittir.","Pi yerine yüzseksen derece yazarak, pi/2 radyan 90 derece, pi/3 radyan 60 derece, pi/4 radyan 45 derece, pi/5 radyan 36 derece, pi/8 radyan 22,5 derece, pi/9 radyan 20 derece, pi/10 radyan 18 derece olarak bulunur.","Pi/3 radyan 120 derece, pi/4 radyan 135 derece, pi/5 radyan 144 derece, pi/6 radyan 150 derece, pi/5 radyan 216 derece, pi/9 radyan 160 derece olarak hesaplanır."]},"beginTime":294,"endTime":383,"href":"/video/preview/8008296315112459252?parent-reqid=1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-BAL&text=Radyan+Design&t=294&ask_summarization=1"},{"index":5,"title":"Radyan ve Derece Dönüşümleri (Devam)","list":{"type":"unordered","items":["Bir radyan yaklaşık 57,30 derecedir.","Yarıçapı bir metre olan bir çemberde bir metrelik yayı gören merkez açı 57,30 derecedir.","Yarıçapı bir metre olan bir çemberde iki metrelik yayı gören merkez açı 114,60 derecedir.","Yarıçapı bir metre olan bir çemberde üç metrelik yayı gören merkez açı 171,30 derecedir.","Yarıçapı iki metre olan bir çemberde iki metrelik yayı gören merkez açı 114,60 derecedir.","Yarıçapı üç metre olan bir çemberde birvirgülelli metrelik yayı gören merkez açı 28,65 derecedir.","Yarıçapı dört metre olan bir çemberde yirmi metrelik yayı gören merkez açı 286,50 derecedir."]},"beginTime":383,"endTime":479,"href":"/video/preview/8008296315112459252?parent-reqid=1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-BAL&text=Radyan+Design&t=383&ask_summarization=1"},{"index":6,"title":"Çemberde Merkez Açı ve Yayın Uzunluğu Hesaplamaları","list":{"type":"unordered","items":["Yarıçapı 8 metre olan bir çemberde 74,49 derecelik merkez açının gördüğü yayın uzunluğu, merkez açının radyan değeri (1,30 radyan) ile yarıçapın çarpımı olan 10,40 metre olarak hesaplanır.","Yarıçapı 12 metre olan bir çemberde 21 metrelik yayı gören merkez açı, yayın uzunluğunun yarıçap oranıyla (1,75 radyan) çarpılarak 102,27 derece olarak bulunur.","27 metrelik yayı gören ve merkez açısı 103,14 derece olan çemberin çapı, yay uzunluğunu merkez açının radyan değerine bölerek (15 metre) yarıçapı bulup, yarıçapın iki katı olan 30 metre olarak hesaplanır."]},"beginTime":481,"endTime":603,"href":"/video/preview/8008296315112459252?parent-reqid=1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-BAL&text=Radyan+Design&t=481&ask_summarization=1"},{"index":7,"title":"Türkiye'nin Dünya Merkezine Göre Açısı","list":{"type":"unordered","items":["Türkiye, 26-45 doğu meridyenleri arasında yer aldığına göre, doğu-batı hizasında kapladığı yüzeyin dünya merkezine göre açısı 19 derece olup, radyan cinsinden 0,33 radyan ve derece cinsinden 18,90 derece olarak hesaplanır.","Türkiye, 36-42 kuzey paralelleri arasında yer aldığına göre, kuzey-güney hizasında kapladığı yüzeyin dünya merkezine göre açısı 6 derece olup, radyan cinsinden 0,10 radyan ve derece cinsinden 5,73 derece olarak bulunur."]},"beginTime":603,"endTime":761,"href":"/video/preview/8008296315112459252?parent-reqid=1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-BAL&text=Radyan+Design&t=603&ask_summarization=1"},{"index":8,"title":"Radyan ve Derece Arasındaki İlişki","list":{"type":"unordered","items":["Bir tekerlek 3,14 radyan döndüğünde yarım tur tamamlamış olur.","Bir tekerlek 6,28 radyan döndüğünde ikinci tur tamamlamış olur.","Bir radyan 57,30 dereceye 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Eğitmen, Flash programında bu ölçü birimlerini nasıl kullanabileceğimizi açıklamaktadır.","Video, radyan ve derece ölçü birimlerinin ne olduğunu, nasıl hesaplandığını ve birbirine nasıl dönüştürüleceğini anlatmaktadır. Önce derece ölçü birimi tanıtılır, bir çemberin 360 dereceye bölündüğü ve bu her bir parçanın bir derece oluşturduğu açıklanır. Ardından radyan ölçü birimi, yarıçapla çevresinin ilişkisi üzerinden anlatılır ve pi sabiti (3.14) kullanılarak radyan hesaplamaları gösterilir. Video, bir sonraki derste radyan ve derece arasındaki dönüşüm formüllerinin nasıl elde edileceğini inceleyeceğini belirterek sona erer."]},"endTime":489,"title":"Radyan ve Derece Ölçü Birimleri Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Radyan ve Derece Kavramları","list":{"type":"unordered","items":["Radyan ve derece, açı ölçü birimi olarak kullanılan iki farklı birimdir.","Derece ilk kullanılan açı ölçü birimidir, daha sonra matematiksel ve teknolojik gelişmelerle radyan da kullanılmaya başlandı.","Radyan ve derece, Flash'ta işlemler yaparken ve birbirine dönüştürme yaparken kullanılır."]},"beginTime":1,"endTime":69,"href":"/video/preview/780852750435569860?parent-reqid=1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-BAL&text=Radyan+Design&t=1&ask_summarization=1"},{"index":1,"title":"Derece Ölçü Birimi","list":{"type":"unordered","items":["Bir çemberin tam çevresi 360 dereceye denk gelir.","Bir çember 360 eşit parçaya bölündüğünde, her bir parçada oluşan açıya bir derece denir.","0, 90, 180, 270 ve 360 derece değerleri çemberin başlangıç noktasına denk gelir ve 360 ve katları her zaman sıfıra eşittir."]},"beginTime":69,"endTime":233,"href":"/video/preview/780852750435569860?parent-reqid=1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-BAL&text=Radyan+Design&t=69&ask_summarization=1"},{"index":2,"title":"Radyan Ölçü Birimi","list":{"type":"unordered","items":["Radyan, yarıçapla çevresinin ilişkisi olarak tanımlanan bir ölçü birimidir.","Pi sabiti (π), çemberin çapının çevresine olan oranını belirtir ve yaklaşık 3,14 değerine sahiptir.","Bir radyan, yarıçapın uzunluğuna eşit olan yayın merkez açısıdır."]},"beginTime":233,"endTime":429,"href":"/video/preview/780852750435569860?parent-reqid=1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-BAL&text=Radyan+Design&t=233&ask_summarization=1"},{"index":3,"title":"Radyan ve Derece Arasındaki 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↔ Derece dönüşümünü artık ezberlemeye gerek yok! 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uzunluğuna eşittir, ancak her durumda açının ölçüsü yayın uzunluğunun yarıçapa oranıdır."]},"beginTime":12,"endTime":105,"href":"/video/preview/10815956765300614684?parent-reqid=1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-BAL&text=Radyan+Design&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 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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":"17","reqid":"1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-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=1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-BAL&text=Radyan+Design&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=1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-BAL&text=Radyan+Design&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=1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-BAL&text=Radyan+Design&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=1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-BAL&text=Radyan+Design&t=202&ask_summarization=1"}],"linkTemplate":"/video/preview/1039435321843030914?parent-reqid=1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-BAL&text=Radyan+Design&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Radyan ve Derece (Trigonometri)","related_orig_text":"Radyan Design","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"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/3924252/3e3f3b104b14c0095695467e4a4c64dc/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/3xK_wwAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"18","reqid":"1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-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=1769479136784114-17278620921612773984-balancer-l7leveler-kubr-yp-klg-185-BAL&text=Radyan+Design&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 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