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Sınıf Matematik: Sinüs ve Kosinüs Teoremleri","beginTime":0}],"fullResult":[{"index":0,"title":"Sinüs ve Kosinüs Teoremleri Giriş","list":{"type":"unordered","items":["Tonguç Akademi 10. sınıf kanalında sinüs ve kosinüs teoremleri konusu ele alınacak.","Öğrenme çıktıları arasında sinüs-kosinüs teoremlerinin doğrulayabilme ve ispatlayabilme, üçgende sinüs ve kosinüs teoremlerine ilişkin farklı doğrulama ve ispatları kullanma, yapılan doğrulama veya ispatları yeni durumlara uyarlayarak değerlendirme bulunmaktadır.","Anahtar kelimeler üçgen, kenar, ikizkenar üçgen, arada kalan açı, sinüs fonksiyonu ve kosinüs fonksiyonudur."]},"beginTime":0,"endTime":79,"href":"/video/preview/5236752796704044973?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=0&ask_summarization=1"},{"index":1,"title":"Sinüs Teoremi","list":{"type":"unordered","items":["Sinüs teoremine göre herhangi bir ABC üçgeninde, her kenar uzunluğu karşısındaki açının sinüs değeri ile doğru orantılıdır.","Formül olarak a/sin(A) = b/sin(B) = c/sin(C) şeklinde ifade edilir.","Sinüs teoremi, sinüs alan formülünden farklı olarak farklı bir formüldür ve alan formülünün temelini oluşturur."]},"beginTime":79,"endTime":179,"href":"/video/preview/5236752796704044973?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=79&ask_summarization=1"},{"index":2,"title":"Sinüs Teoremi Örnekleri","list":{"type":"unordered","items":["İlk örnekte, ABC üçgeninde BC açısı 30 derece, AB uzunluğu 8√3 cm ve BC uzunluğu 8 cm olduğunda, ACB açısının (α) 60 derece olduğu bulunmuştur.","İkinci örnekte, ABC üçgeninde A açısı 45 derece, B açısı 60 derece ve AC uzunluğu 3√2 cm olduğunda, BC uzunluğunun 3√3 cm olduğu hesaplanmıştır.","Üçüncü örnekte, ABC üçgeninde AC uzunluğu 16 cm, BC uzunluğu 20 cm ve α-β=90° olduğunda, tan(ABC) değeri 4/5 olarak bulunmuştur."]},"beginTime":179,"endTime":613,"href":"/video/preview/5236752796704044973?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=179&ask_summarization=1"},{"index":3,"title":"Dik Üçgende Pisagor Bağıntısı ve Benzerlik","list":{"type":"unordered","items":["Dik üçgende Pisagor bağıntısı kullanılarak BC kenarının uzunluğu kök beş olarak hesaplanmıştır.","Üçgende benzerlik kurularak kenar uzunlukları belirlenmiştir.","Sinüs teoremi kullanılarak EDC açısının (beta) 30 derece olduğu bulunmuştur."]},"beginTime":615,"endTime":795,"href":"/video/preview/5236752796704044973?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=615&ask_summarization=1"},{"index":4,"title":"Sinüs Teoreminin İspatı","list":{"type":"unordered","items":["Sinüs alan formülü kullanılarak üç farklı şekilde üçgenin alanı hesaplanmıştır: 1/2 × bc × sin a, 1/2 × ab × sin c ve 1/2 × ac × sin b.","Bu üç formül birbirine eşitlenerek b × sin a = a × sin b ve c × sin a = a × sin c çıkarımları elde edilmiştir.","Bu çıkarımlar birleştirilerek sinüs teoremi (a/sin A = b/sin B = c/sin C) ispatlanmıştır."]},"beginTime":795,"endTime":1103,"href":"/video/preview/5236752796704044973?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=795&ask_summarization=1"},{"index":5,"title":"Sinüs Teoremi Örneği","list":{"type":"unordered","items":["ABC üçgeninin çevresi 52 santimetre olarak verilmiştir.","sin A = 2, sin B = 3 ve sin C = 4 olarak ifade edilmiştir.","Bu orantılar 12'nin katları olarak yorumlanarak sin A = 12 × 2, sin B = 12 × 3 ve sin C = 12 × 4 şeklinde yazılabilir."]},"beginTime":1103,"endTime":1157,"href":"/video/preview/5236752796704044973?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=1103&ask_summarization=1"},{"index":6,"title":"Sinüs Teoremi Uygulaması","list":{"type":"unordered","items":["Üçgenin çevresi 52 santimetre olduğunda, a+b+c=52 denklemi kurulabilir.","Sinüs teoremi uygulanarak a/sinA = b/sinB = c/sinC ilişkisi elde edilir.","Orantı teoremi kullanılarak c/sinC = (52-c)/sin(A+B) denklemi kurulur ve sin(A+B) = sinA + sinB = 6k olarak hesaplanır."]},"beginTime":1161,"endTime":1305,"href":"/video/preview/5236752796704044973?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=1161&ask_summarization=1"},{"index":7,"title":"Denklem Çözümü","list":{"type":"unordered","items":["c = 3k ve sin(A+B) = 10k olarak yerine yazılıp denklem düzenlenir.","İçler dışlar çarpımı yapılarak 10c = 3(52-3c) denklemi elde edilir.","Denklem çözülürse c = 12 cm olarak bulunur."]},"beginTime":1305,"endTime":1369,"href":"/video/preview/5236752796704044973?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=1305&ask_summarization=1"},{"index":8,"title":"Kosinüs Teoremi","list":{"type":"unordered","items":["Kosinüs teoremi: a² = b² + c² - 2bc·cosA şeklinde ifade edilir.","Bir üçgende iki kenar uzunluğu ve bu kenarlar arasındaki açının kosinüsü bilindiğinde, diğer kenar uzunluğu bulunabilir.","Kosinüs teoremi ile b² = a² + c² - 2ac·cosB ve c² = a² + b² - 2ba·cosC formülleri de elde edilir."]},"beginTime":1369,"endTime":1450,"href":"/video/preview/5236752796704044973?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=1369&ask_summarization=1"},{"index":9,"title":"Kosinüs Teoremi Uygulaması","list":{"type":"unordered","items":["ABC üçgeninde B açısı 60 derece, AB uzunluğu 2 cm, BC uzunluğu 3 cm olduğunda AC uzunluğu bulunur.","AC² = 2² + 3² - 2·2·3·cos60° formülü kullanılarak hesaplanır.","AC² = 7 bulunur ve AC = √7 cm olarak hesaplanır."]},"beginTime":1450,"endTime":1554,"href":"/video/preview/5236752796704044973?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=1450&ask_summarization=1"},{"index":10,"title":"İkinci Kosinüs Teoremi Sorusu","list":{"type":"unordered","items":["ABC ve ACD üçgenlerinde AB = 8 cm, AC = 6 cm, CD = 5 cm olduğunda A uzunluğu bulunur.","BC uzunluğu 10 cm olarak belirlenir ve kosinüs teoremi uygulanır.","Kosinüs teoremi kullanılarak A² = 64 + 225 - 192 = 97 bulunur ve A = √97 cm olarak hesaplanır."]},"beginTime":1554,"endTime":1699,"href":"/video/preview/5236752796704044973?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=1554&ask_summarization=1"},{"index":11,"title":"Kosinüs Teoremi Uygulaması","list":{"type":"unordered","items":["ABC ve A birer üçgen olup, AB=3 cm, AC=5 cm, BC=3 cm ve DE uzunluğu soruluyor.","Kosinüs teoremi kullanılarak A açısının kosinüsü bulunuyor: cos A = 5/6.","Bulunan kosinüs değeri kullanılarak DE uzunluğu hesaplanıyor: DE = √15 cm."]},"beginTime":1707,"endTime":1880,"href":"/video/preview/5236752796704044973?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=1707&ask_summarization=1"},{"index":12,"title":"İkinci Kosinüs Teoremi Sorusu","list":{"type":"unordered","items":["ABC ve DC birer üçgen olup, AC=3 cm, DC=7 cm, DE=13 cm, BC=14 cm ve AC=10 cm verilmiş.","Kosinüs teoremi kullanılarak önce DC üçgeninde cos α değeri bulunuyor: cos α = -1/7.","Bulunan cos α değeri kullanılarak ABC üçgeninde AB uzunluğu hesaplanıyor: AB = 16 cm."]},"beginTime":1880,"endTime":2118,"href":"/video/preview/5236752796704044973?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=1880&ask_summarization=1"},{"index":13,"title":"Kosinüs Teoreminin İspatı","list":{"type":"unordered","items":["ABC üçgeninde bir yükseklik indirilerek iki Pisagor bağıntısı kuruluyor: h² = c² - x² ve h² = a² - (b-x)².","İki Pisagor bağıntısı birbirine eşitlenerek c² = a² + b² + 2bc cos A ilişkisi elde ediliyor.","Kos A = x/c ilişkisi kullanılarak c² = a² + b² + c² - 2bc cos A sonucuna ulaşılıyor."]},"beginTime":2118,"endTime":2466,"href":"/video/preview/5236752796704044973?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=2118&ask_summarization=1"}],"linkTemplate":"/video/preview/5236752796704044973?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Sinüs ve Kosinüs Teoremleri | 10. 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Koordinat Düzleminde \"y\" ekseni olarak tabir edilir.Bu işlevin tanım aralığı [-1,1] dir. Yani, Sinx -1 den küçük 1 den...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/399189/a228b2132ff6ccba02098beb3577706f/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/HCeCDQAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"1","reqid":"1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=videoid:5443788018975714578","teaser":[{"list":{"type":"unordered","items":["Bu video, Tonguç Akademi'de bir öğretmen ve Tonguç adlı bir öğrenci arasında geçen trigonometri dersidir. Öğretmen, trigonometrik oranlar konusunu anlatmaktadır.","Video, sinüs ve kosinüs kavramlarının tanımıyla başlayıp, dik üçgende sinüs ve kosinüsün nasıl hesaplandığını açıklamaktadır. Öğretmen, sinüs ve kosinüsün değerlerini hatırlamak için \"Sinan\" ve \"Tanya\" gibi kısayollar kullanmaktadır. Daha sonra sin²x + cos²x = 1 ve tan²x + cot²x = 1 gibi trigonometrik özdeşlikler anlatılmakta ve bunların uygulamaları gösterilmektedir. Son olarak, sinüs ve kosinüsün alabileceği değerler (0 ile 1 arasında) ve bunların toplamı veya farkı gibi konular ele alınmaktadır."]},"endTime":446,"title":"Trigonometri Dersi: Sinüs ve Kosinüs","beginTime":0}],"fullResult":[{"index":0,"title":"Trigonometrik Oranlar: Sinüs ve Kosinüs","list":{"type":"unordered","items":["Trigonometri'de sinüs ve kosinüs konusu işlenecek.","Sinüs, dik üçgende bir açının karşısındaki kenarın hipotenüse oranıdır (karşı/hipotenüs).","Kosinüs, dik üçgende bir açının komşusundaki kenarın hipotenüse oranıdır (komşu/hipotenüs)."]},"beginTime":0,"endTime":80,"href":"/video/preview/5443788018975714578?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=0&ask_summarization=1"},{"index":1,"title":"Özel Üçgenler ve Örnek Soru","list":{"type":"unordered","items":["Özel üçgenler hatırlatılıyor: 3-4-5, 5-12-13 gibi.","5-12-13 üçgeninde sinx = 12/13 ve cosx = 5/13 olarak hesaplanıyor.","Sinx + cosx = 17/13 olarak bulunuyor."]},"beginTime":80,"endTime":145,"href":"/video/preview/5443788018975714578?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=80&ask_summarization=1"},{"index":2,"title":"Trigonometrik Kimlikler","list":{"type":"unordered","items":["Sin²x + cos²x = 1 kimliği geçerlidir.","Sinx × cosx sorusu için önce her iki tarafın karesi alınır.","(sinx + cosx)² = 1 + 2sinx × cosx formülü kullanılarak sinx × cosx = 12/25 olarak bulunur."]},"beginTime":145,"endTime":286,"href":"/video/preview/5443788018975714578?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=145&ask_summarization=1"},{"index":3,"title":"Sinüs ve Kosinüsün Değer Aralığı","list":{"type":"unordered","items":["Sinüs ve kosinüs fonksiyonları her zaman -1 ile 1 arasında değer alır.","3sinx - 5cosx ifadesinin maksimum değeri 8, minimum değeri -8'dir.","Maksimum değer için sinx = 1 ve cosx = -1, minimum değer için sinx = -1 ve cosx = 1 alınır."]},"beginTime":286,"endTime":440,"href":"/video/preview/5443788018975714578?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=286&ask_summarization=1"}],"linkTemplate":"/video/preview/5443788018975714578?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"7dk'da Trigonometri Sinüs VE Kosinüs","related_orig_text":"sinus hd","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"sinus 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ve özdeşlikler konumuzla başlayıp tüm konu ve temaları hızlıca işleyeceğiz.","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2850481/99f904401021d79d03f034040b473f50/564x318_1"},"target":"_self","position":"2","reqid":"1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=videoid:1670934552690531911","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik öğretmeninin 10. sınıf öğrencilerine yönelik hazırladığı eğitim içeriğidir. Öğretmen, sinüs ve kosinüs teoremlerini detaylı bir şekilde anlatmaktadır.","Video, sinüs teoreminin ne olduğu ve formülüyle başlayıp, çeşitli örnek sorular üzerinden uygulamalarını göstermektedir. Ardından kosinüs teoremi anlatılmakta ve formülleri (a² = b² + c² - 2bc cosA ve b² = a² + c² - 2ac cosB) açıklanmaktadır. Son bölümde ise sinüs ve kosinüs teoremlerinin birlikte kullanıldığı karmaşık sorular çözülmektedir.","Videoda açı hesaplamaları, harita üzerinde uzaklık bulma, çadırın üçgen şeklinde görünümü üzerinden oran hesaplaması, dikme kaldırma problemi, merdivenlerle binanın çatısına çıkabilme problemi ve eş ayaklı merdivenlere bağlanan lastiklerin uzunluğunu bulma gibi çeşitli uygulamalar ele alınmaktadır. Öğretmen, sınavlarda çıkabilecek soru tiplerini vurgulayarak, özellikle hem sinüs hem kosinüs teoremini içeren karmaşık soruları da çözmektedir."]},"endTime":3204,"title":"10. Sınıf Matematik: Sinüs ve Kosinüs Teoremi Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Sinüs ve Kosinüs Teoremi Tanıtımı","list":{"type":"unordered","items":["Bu videoda sinüs ve kosinüs teoremi konuları bir videoda ele alınacak ve bu konulardan mutlaka soru gelecektir.","Sinüs teoremi, bir açı ve karşısındaki sinüsü, başka bir kenar ve karşısındaki sinüsü biliyorsak, bu oranların birbirine eşit olduğunu gösterir.","Sinüs teoremi, açıların sinüslerini veya kenarların uzunluklarını hesaplamak için kullanılır."]},"beginTime":0,"endTime":111,"href":"/video/preview/1670934552690531911?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=0&ask_summarization=1"},{"index":1,"title":"Özel Açıların Sinüs Değerleri","list":{"type":"unordered","items":["Sinüs teoremi kullanabilmek için özel açıların sinüs değerlerini bilmek gerekir: 30°, 45°, 60° ve 90° açılarının sinüs değerleri sırasıyla 1/2, √2/2, √3/2 ve 1'dir.","Sinüs değerlerini hatırlamak için \"30-45-60\" sırasını kullanıp, altına 2 yazıp üstüne 1, 2, 3 yazıp karekök koyarak hesaplanabilir.","120°, 150° ve 180° açılarının sinüs değerleri, 60°, 45° ve 30° açılarının sinüs değerlerine eşittir."]},"beginTime":111,"endTime":194,"href":"/video/preview/1670934552690531911?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=111&ask_summarization=1"},{"index":2,"title":"Sinüs Teoremi Örnekleri","list":{"type":"unordered","items":["İlk örnekte, 2√3 kenarı ve karşısındaki 120° açının sinüsü bilindiğinde, x kenarının uzunluğu 2√2 olarak hesaplanır.","İkinci örnekte, 6° kenarı ve sinüs alfa değeri bilindiğinde, sinüs beta değeri 9/5 olarak bulunur.","Üçüncü örnekte, 7° kenarı ve sinüs teta değeri bilindiğinde, sinüs alfa değeri 6/7 olarak hesaplanır.","Dördüncü örnekte, 7° kenarı ve sinüs beta değeri bilindiğinde, sinüs beta'nın sinüs teta'ya oranı 7/5 olarak bulunur."]},"beginTime":194,"endTime":604,"href":"/video/preview/1670934552690531911?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=194&ask_summarization=1"},{"index":3,"title":"Sinüs Teoremi ile Açı Hesaplama","list":{"type":"unordered","items":["Üçgende sinüs teoremi kullanılarak açılar hesaplanıyor ve sinüs beta ile sinüs (180-beta) arasındaki ilişki kullanılıyor.","Sinüs teoremi uygulandıktan sonra ifadeler taraf tarafa bölünerek sadeleştirme yapılıyor.","Sinüs alfa değeri √2/5 olarak bulunuyor."]},"beginTime":606,"endTime":815,"href":"/video/preview/1670934552690531911?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=606&ask_summarization=1"},{"index":4,"title":"Harita Problemi","list":{"type":"unordered","items":["Haritada ABC üçgeninin köşelerindeki yerleşim yerlerinin konumları ve bazı açı değerleri verilmiş.","Üçgenin iç açıları toplamı 180 derece olduğundan, verilen açılar kullanılarak üçüncü açı 74 derece olarak hesaplanıyor.","B ile C arasındaki uzaklık 480 metre olduğunda, A ile B arasındaki uzaklık 370 metre olarak bulunuyor."]},"beginTime":815,"endTime":978,"href":"/video/preview/1670934552690531911?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=815&ask_summarization=1"},{"index":5,"title":"Çadır Problemi","list":{"type":"unordered","items":["Çadırın üçgen şeklinde önden görünümü verilmiş ve BD'nin 4 katı DC'ye eşit olduğu belirtilmiş.","Sinüs teoremi kullanılarak AB'nin AC'ye oranı hesaplanıyor.","AB'nin AC'ye oranı √2/4 olarak bulunuyor."]},"beginTime":978,"endTime":1175,"href":"/video/preview/1670934552690531911?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=978&ask_summarization=1"},{"index":6,"title":"Kosinüs Teoremi ve Kullanım Alanları","list":{"type":"unordered","items":["Kosinüs teoremi, bir üçgende iki kenar ve aralarındaki açının kosinüsünü biliyorsak üç kenarı hesaplamak için kullanılır.","Kosinüs teoremi ayrıca, üçgenin üç kenarını biliyorsak istenen açının kosinüs değerini hesaplamak için de kullanılabilir.","Kosinüs teoremi, Pisagor bağıntısının özel bir halidir; açı 90 derece olduğunda Pisagor bağıntısına dönüşür."]},"beginTime":1177,"endTime":1262,"href":"/video/preview/1670934552690531911?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=1177&ask_summarization=1"},{"index":7,"title":"Kosinüs Teoremi Formülleri","list":{"type":"unordered","items":["Bir kenarı hesaplamak için: a² = b² + c² - 2bc·cos(A) formülü kullanılır.","Diğer kenarı hesaplamak için: b² = a² + c² - 2ac·cos(B) formülü kullanılır.","Formülleri ezberlemek yerine, hangi kenarı hesaplamak istediğimizi mantığıyla düşünerek formülü kullanabiliriz."]},"beginTime":1262,"endTime":1334,"href":"/video/preview/1670934552690531911?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=1262&ask_summarization=1"},{"index":8,"title":"Kosinüs Teoremi Örnekleri","list":{"type":"unordered","items":["Örnek 1: 7, 8 ve 10 derecelik açılı üçgende x kenarını hesaplamak için: x² = 7² + 8² - 2·7·8·cos(60) = 57, x = √57 bulunur.","Örnek 2: 7, 8 ve 10 derecelik açılı üçgende alfa açısının kosinüsünü hesaplamak için: 10² = 7² + 8² - 2·7·8·cos(alfa), cos(alfa) = 13/112 bulunur."]},"beginTime":1334,"endTime":1491,"href":"/video/preview/1670934552690531911?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=1334&ask_summarization=1"},{"index":9,"title":"Kosinüs Değerleri","list":{"type":"unordered","items":["Kosinüs 30° = sinüs 60° = √2/2, kosinüs 60° = sinüs 30° = 1/2, kosinüs 90° = 0'dır.","Geniş açıların kosinüs değerleri, küçük açıların kosinüs değerlerine eşittir ancak başına eksi işareti gelir.","Örneğin, kosinüs 120° = -cos(60°), kosinüs 135° = -cos(45°), kosinüs 150° = -cos(30°) olur."]},"beginTime":1491,"endTime":1565,"href":"/video/preview/1670934552690531911?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=1491&ask_summarization=1"},{"index":10,"title":"Kosinüs Teoremi ile Açı Hesaplamaları","list":{"type":"unordered","items":["Kosinüs teoremi kullanılarak alfa ve beta açılarının kosinüs değerleri hesaplanıyor.","Alfa açısının kosinüsü için 8² = 5² + 7² - 2·5·7·cos(alfa) denklemi çözülerek cos(alfa) = 1/7 bulunuyor.","Beta açısının kosinüsü için 7² = 5² + 8² - 2·5·8·cos(beta) denklemi çözülerek cos(beta) = 1/2 bulunuyor."]},"beginTime":1568,"endTime":1734,"href":"/video/preview/1670934552690531911?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=1568&ask_summarization=1"},{"index":11,"title":"Direk Problemi","list":{"type":"unordered","items":["Uzunluğu 8 metre olan bir direk, zemin üzerinde iken yer ile alfa derecelik açı yapacak biçimde kaldırılıyor.","Direğin sağ ucundaki önceki durumdaki konumuna uzaklığı (x) hesaplanıyor.","Kosinüs alfa = 3/4 verildiğinde, x² = 8² + 8² - 2·8·8·cos(alfa) denklemi çözülerek x = 4√2 bulunuyor."]},"beginTime":1734,"endTime":1824,"href":"/video/preview/1670934552690531911?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=1734&ask_summarization=1"},{"index":12,"title":"Diğer Problemler","list":{"type":"unordered","items":["x'in karesi = 4² + 6² - 2·4·6²·cos(60) denklemi çözülerek x = 2√7 bulunuyor.","ABC üçgeninde AC uzunluğu hesaplanacak.","Geniş açılar için kosinüs değeri eksi işaretine dönüşür."]},"beginTime":1824,"endTime":1895,"href":"/video/preview/1670934552690531911?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=1824&ask_summarization=1"},{"index":13,"title":"Kosinüs Teoremi Uygulamaları","list":{"type":"unordered","items":["Kosinüs teoremi kullanılarak x² = 3² + 2√3² - 2·3·2√3·cos(120) denklemi çözülüyor ve x = √21 olarak bulunuyor.","ABC üçgeninde AB=3, AC=7, BC=9 olduğunda A açısının kosinüsü cos(alfa) = -23/42 olarak hesaplanıyor.","Dik üçgende Pisagor bağıntısı kullanılarak hipotenüs hesaplanıyor ve kosinüs teoremi ile x² = 57 bulunuyor, x = √57 olarak hesaplanıyor."]},"beginTime":1897,"endTime":2251,"href":"/video/preview/1670934552690531911?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=1897&ask_summarization=1"},{"index":14,"title":"Kosinüs Teoremi ile Açı Hesaplama","list":{"type":"unordered","items":["ABC üçgeninde B açısının ölçüsü için kosinüs teoremi kullanılarak cos(alfa) = 1/2 bulunuyor ve alfa = 60° olarak hesaplanıyor.","KCD üçgeninin alanını hesaplamak için önce kosinüs teoremi ile cos(beta) = 1/2 bulunuyor, sonra sinüs teoremi ile alan hesaplanıyor.","Kosinüs teoreminin en yaygın kullanımlarından biri, kayıkların hareketiyle oluşan uzaklıkları hesaplamaktır."]},"beginTime":2251,"endTime":2729,"href":"/video/preview/1670934552690531911?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=2251&ask_summarization=1"},{"index":15,"title":"Sınavlık Sorular","list":{"type":"unordered","items":["Son üç soru sınavlık sorular olarak belirtiliyor.","Soruda hem sinüs teoremi hem kosinüs teoremi kullanılıyor.","Salih'in mantar ponuna yapıştırdığı iplerle oluşan üçgenler inceleniyor."]},"beginTime":2729,"endTime":2741,"href":"/video/preview/1670934552690531911?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=2729&ask_summarization=1"},{"index":16,"title":"Sinüs ve Kosinüs Teoremi Uygulamaları","list":{"type":"unordered","items":["C ve D noktaları arasına takılan ipin uzunluğunu bulmak için önce sinüs teoremi kullanılarak y kenarı hesaplanır.","Sinüs teoremi ile y = 16/sin(36) = 16/0,8 = 18 olarak bulunur.","Kosinüs teoremi uygulanarak x² = 10² + 8² - 2·10·18·cos(72) = 100 + 64 - 108·0,3 = 316 olarak hesaplanır ve x = √316 bulunur."]},"beginTime":2750,"endTime":2900,"href":"/video/preview/1670934552690531911?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=2750&ask_summarization=1"},{"index":17,"title":"Merdiven Problemi","list":{"type":"unordered","items":["İki merdiven ile binanın çatısına çıkabilme problemi için sinüs teoremi kullanılır.","Büyük dik üçgende sinüs beta = 12/20 = 3/5 olarak hesaplanır.","Sinüs teoremi ile 11/sin(alfa) = 13/3/5 denkleminden sin(alfa) = 33/65 bulunur."]},"beginTime":2900,"endTime":3016,"href":"/video/preview/1670934552690531911?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=2900&ask_summarization=1"},{"index":18,"title":"Merdiven ve Lastik Problemi","list":{"type":"unordered","items":["Merdivenin eş ayakları arasına bağlanan iki lastikten alttaki lastiğin uzunluğu bulunur.","Küçük üçgende kosinüs teoremi uygulanarak cos(alfa) = 11/16 olarak hesaplanır.","Büyük üçgende kosinüs teoremi uygulanarak x² = 100 + 64 - 100 × 8 × 11/16 = 54 olarak bulunur ve x = 3√6 bulunur."]},"beginTime":3016,"endTime":3169,"href":"/video/preview/1670934552690531911?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=3016&ask_summarization=1"},{"index":19,"title":"Dersin Kapanışı","list":{"type":"unordered","items":["Tek videoda sinüs ve kosinüs konuları tamamlanmış ve sınavda karşınıza gelebilecek sorular çözülmüştür.","Daha sonra özetler ve tekrar videosu, yazılı senaryosu hazırlanacaktır.","Uzun videoları izleyenler bilgiye tam donanımlı olarak gelirken, sadece tekrar videolarını izleyenler günü kurtarırlar."]},"beginTime":3169,"endTime":3203,"href":"/video/preview/1670934552690531911?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=3169&ask_summarization=1"}],"linkTemplate":"/video/preview/1670934552690531911?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Sinüs -Kosinüs teoremleri -10. 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Konuşmacı, görsel materyaller kullanarak para nazal sinüslerini anlatmaktadır.","Video, para nazal sinüslerinin tanımı ve konumlarıyla başlayıp, görevlerini açıklamaktadır. Daha sonra sinüslerin anatomik yapısı, gelişim süreçleri ve fizyolojik özellikleri detaylı olarak ele alınmaktadır. Özellikle sinüs maksillaris, sinüs frontalis, sinüs etmoidalis ve sinüs sfenoidalis gibi farklı sinüs türleri ve bunların anatomik ilişkileri, besleyen arterler, drenaj yolları ve enfeksiyonlarda dikkat edilmesi gereken noktalar üzerinde durulmaktadır. Video, sinüslerin fizyolojik fonksiyonlarını ve patolojik durumları anlamanı sağlayan kapsamlı bir anlatımdır."]},"endTime":2015,"title":"Para Nazal Sinüsleri Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Paranazal Sinüslerin Tanımı ve Konumu","list":{"type":"unordered","items":["Paranazal sinüsler, burun boşluğunun etrafında bulunan ve burun boşluğuyla direkt bağlantılı olan boşluklardır.","Burun boşluğu septum nasi tarafından iki kısma ayrılır ve dış duvarı ile iç duvarı vardır.","En büyük paranazal sinüs maksillaris'tir ve ağzı burun boşluğunun dış duvarında yer alır."]},"beginTime":2,"endTime":82,"href":"/video/preview/13835332684310944558?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=2&ask_summarization=1"},{"index":1,"title":"Paranazal Sinüslerin Türleri","list":{"type":"unordered","items":["Paranazal sinüsler arasında frontal sinüs, sfenoid sinüs ve etmoid sinüsler (selüla etmoidesler) bulunmaktadır.","Paranazal sinüsler burun mugozasının kemikler içerisine girmesiyle veya gömülmesiyle oluşan boşluklardır.","Bu sinüsler baş ağrılarını azaltır, beynin ısısını korur, aksırırken artan burun içi basıncını azaltır ve ses rezonansını kuvvetlendirir."]},"beginTime":82,"endTime":148,"href":"/video/preview/13835332684310944558?parent-reqid=1766619406255941-9834596648576905985-balancer-l7leveler-kubr-yp-sas-89-BAL&text=sinus+hd&t=82&ask_summarization=1"},{"index":2,"title":"Paranazal Sinüslerin Görevleri","list":{"type":"unordered","items":["Paranazal sinüsler havayı süzerek ısıtır ve nemlendirir, burun boşluğuna yardımcı olurlar.","Bu sinüsler diş kökleri ve göz gibi yapıları burun boşluğundaki ani ısı ardıçlarından korur.","Paranazal sinüslerin projeksiyonları yüzümüzün dışından baktığımızda 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