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Sınıf Matematik: Trigonometri Dersi - Sinüs ve Kosinüs Fonksiyonları","beginTime":0}],"fullResult":[{"index":0,"title":"Trigonometrik Fonksiyonlar Dersi Tanıtımı","list":{"type":"unordered","items":["11. sınıf matematik dersinde trigonometrik fonksiyonlar konusuna giriş yapılıyor.","Bu videoda sinüs ve kosinüs fonksiyonları anlatılacak, bir sonraki videoda tanjant ve kotanjant fonksiyonlarına değinilecek.","Ders, kitabın 10. sayfadan başlayarak birim çemberde trigonometrik fonksiyonlar konusunu ele alacak."]},"beginTime":0,"endTime":70,"href":"/video/preview/17089670257672128761?parent-reqid=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-BAL&text=sinus+hd&t=0&ask_summarization=1"},{"index":1,"title":"Birim Çemberde Kosinüs ve Sinüs Fonksiyonları","list":{"type":"unordered","items":["Birim çemberde alfa açısının OP doğru parçasının çemberi kestiği noktaya P noktası denir.","P noktasının apsisi (x koordinatı) alfa açısının kosinüsü olarak adlandırılır ve cos α ile gösterilir.","P noktasının ordinatı (y koordinatı) alfa açısının sinüsü olarak adlandırılır ve sin α ile gösterilir."]},"beginTime":70,"endTime":221,"href":"/video/preview/17089670257672128761?parent-reqid=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-BAL&text=sinus+hd&t=70&ask_summarization=1"},{"index":2,"title":"Kosinüs ve Sinüs Fonksiyonlarının Özellikleri","list":{"type":"unordered","items":["Kosinüs ve sinüs, uzunluk değil, koordinat belirtir ve bu nedenle negatif olabilir.","Birim çemberde P noktasının koordinatları (cos α, sin α) şeklinde ifade edilir.","Sinüs ve kosinüsün kareleri toplamı her zaman 1'e eşittir: sin²α + cos²α = 1."]},"beginTime":221,"endTime":362,"href":"/video/preview/17089670257672128761?parent-reqid=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-BAL&text=sinus+hd&t=221&ask_summarization=1"},{"index":3,"title":"Açı Değişimlerinde Kosinüs ve Sinüs Değerlerinin Davranışı","list":{"type":"unordered","items":["Açı büyüdükçe P noktasının konumu değişir ve bu değişme kosinüs ve sinüs değerlerini etkiler.","Açı arttıkça kosinüs değeri küçülür, açı 90 dereceye ulaştığında kosinüs değeri sıfıra eşit olur.","Açı 90 dereceden büyük olduğunda, P noktası birim çemberin sol tarafında olur ve kosinüs değeri negatif olur."]},"beginTime":362,"endTime":444,"href":"/video/preview/17089670257672128761?parent-reqid=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-BAL&text=sinus+hd&t=362&ask_summarization=1"},{"index":4,"title":"Birim Çemberde Kosinüs ve Sinüs Değerleri","list":{"type":"unordered","items":["Birim çember üzerindeki bir noktanın apsisi kosinüs değerini, ordinatı sinüs değerini verir.","Kosinüs değeri 1'den başlayıp, 0'a, -1'e, tekrar 0'a ve 1'e gelerek değişir.","Sinüs değeri de 1'den başlayıp, 0'a, -1'e, tekrar 0'a ve 1'e gelerek değişir."]},"beginTime":446,"endTime":611,"href":"/video/preview/17089670257672128761?parent-reqid=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-BAL&text=sinus+hd&t=446&ask_summarization=1"},{"index":5,"title":"Kosinüs ve Sinüsün Maksimum ve Minimum Değerleri","list":{"type":"unordered","items":["Kosinüs ve sinüs fonksiyonlarının maksimum değeri 1, minimum değeri -1'dir.","Kosinüs ve sinüs fonksiyonları herhangi bir açı için -1'den küçük veya 1'den büyük değer alamaz.","Birim çember üzerindeki bir noktanın ordinatı sinüs değerini verir."]},"beginTime":611,"endTime":741,"href":"/video/preview/17089670257672128761?parent-reqid=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-BAL&text=sinus+hd&t=611&ask_summarization=1"},{"index":6,"title":"Örnek Sorular","list":{"type":"unordered","items":["f(x) = 5sinx - 2 fonksiyonunun alabileceği tam sayı değerleri -7'den 3'e kadar olan 11 farklı tam sayıdır.","4 - 2sinx/3 ifadesinin alabileceği en geniş değer aralığı 1/3 ile 2 arasındadır.","Bir ifadenin en büyük değerini bulmak için pozitif terimlere en büyük değer, negatif terimlere en küçük değer verilmelidir."]},"beginTime":741,"endTime":919,"href":"/video/preview/17089670257672128761?parent-reqid=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-BAL&text=sinus+hd&t=741&ask_summarization=1"},{"index":7,"title":"Trigonometrik Fonksiyonların En Büyük ve En Küçük Değerleri","list":{"type":"unordered","items":["Sinüs fonksiyonunun alabileceği en büyük değer 1, kosinüs fonksiyonunun alabileceği en küçük değer -1'dir.","3sinx - 2cosy + 1 ifadesinin en büyük değeri 6, en küçük değeri -4'tür.","En büyük değer (6) en küçük değerden (4) 10 fazladır."]},"beginTime":933,"endTime":1006,"href":"/video/preview/17089670257672128761?parent-reqid=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-BAL&text=sinus+hd&t=933&ask_summarization=1"},{"index":8,"title":"Kosinüs Fonksiyonunun Değer Aralığı","list":{"type":"unordered","items":["Kosinüs fonksiyonunun her zaman -1'den büyük ve 1'den küçük değerler alır.","7 - cos3x/2 ifadesinin değer aralığı 3 ≤ k ≤ 4'tür.","k'nın alabileceği tam sayı değerlerinin toplamı 3 + 4 = 7'dir."]},"beginTime":1006,"endTime":1112,"href":"/video/preview/17089670257672128761?parent-reqid=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-BAL&text=sinus+hd&t=1006&ask_summarization=1"},{"index":9,"title":"Fonksiyonların Değerleri ve Çarpımları","list":{"type":"unordered","items":["f(t) = (t² - 36)/(t - 6) fonksiyonu, t ≠ 6 olmak üzere f(t) = t + 6 şeklinde sadeleştirilir.","f(1 + 3cosα) ifadesinin en büyük değeri 10, en küçük değeri 4'tür.","En büyük ve en küçük değerlerin çarpımı 10 × 4 = 40'dır."]},"beginTime":1112,"endTime":1191,"href":"/video/preview/17089670257672128761?parent-reqid=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-BAL&text=sinus+hd&t=1112&ask_summarization=1"},{"index":10,"title":"Mutlak Değerli İfadelerin Sadeleştirilmesi","list":{"type":"unordered","items":["|1 - cosx| ifadesinde, cosx maksimum 1 olduğundan, 1 - cosx her zaman pozitif olduğu için mutlak değer dışına 1 - cosx olarak çıkar.","|sinx| ifadesinde, sinx minimum -1 olduğundan, mutlak değer dışına -sinx olarak çıkar.","|4 - cosx + sinx| ifadesi her zaman pozitif olduğu için kendi gibi çıkar, ancak önünde eksi olduğu için içine dağılır."]},"beginTime":1191,"endTime":1339,"href":"/video/preview/17089670257672128761?parent-reqid=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-BAL&text=sinus+hd&t=1191&ask_summarization=1"},{"index":11,"title":"Trigonometrik İfadelerin Değer Aralığı","list":{"type":"unordered","items":["4sin²3x - 2 ifadesinin en geniş değer aralığı bulunurken, sin3x'in değer aralığı -1 ≤ sin3x ≤ 1'dir.","sin²3x'in değer aralığı 0 ≤ sin²3x ≤ 1'dir.","4sin²3x - 2 ifadesinin değer aralığı -2 ≤ 4sin²3x - 2 ≤ 2'dir."]},"beginTime":1339,"endTime":1425,"href":"/video/preview/17089670257672128761?parent-reqid=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-BAL&text=sinus+hd&t=1339&ask_summarization=1"},{"index":12,"title":"Trigonometrik İfadelerin En Büyük ve En Küçük Değerleri","list":{"type":"unordered","items":["a.sinx + b.cosx ifadesinin en büyük değerini bulurken, açılar aynı olduğunda sinüs ve kosinüsün en büyük değerlerini 1 olarak alamazsınız.","a.sinx + b.cosx ifadesinin en büyük değeri √(a² + b²), en küçük değeri -√(a² + b²)'dir.","Bu özellik doksan günde AYT matematik kampında ve kitapta trigonometri kısmında ispatlanmıştır."]},"beginTime":1425,"endTime":1540,"href":"/video/preview/17089670257672128761?parent-reqid=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-BAL&text=sinus+hd&t=1425&ask_summarization=1"},{"index":13,"title":"Trigonometrik İfadelerin Değer Aralıkları","list":{"type":"unordered","items":["Üç sinx eksi dört kosinüs x ifadesinin en geniş değer aralığı, en büyük değeri (5) ve en küçük değeri (−5) bulunarak [−5, 5] olarak hesaplanmıştır.","Beş kos x artı oniki sx ifadesinin alabileceği tam sayı değerleri, en küçük değeri (−13) ve en büyük değeri (13) arasında 27 tane olduğu belirlenmiştir.","Koskara eksi dört skos artı dört sinkare ifadesinin en büyük değeri, ifadenin (cosx − 2sinx)² şeklinde yazılabilmesiyle ve iç parantezin en büyük değerin (√5) karesinin alınmasıyla 5 olarak bulunmuştur."]},"beginTime":1542,"endTime":1773,"href":"/video/preview/17089670257672128761?parent-reqid=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-BAL&text=sinus+hd&t=1542&ask_summarization=1"},{"index":14,"title":"Öğrenme Önerileri","list":{"type":"unordered","items":["Kitap doldururken her şeyi anlayarak yapmanın öneminden bahsedilmiştir.","Video kayıtlarının tekrar tekrar izlenebilirliği, derslerin daha iyi anlaşılmasını sağlayacak bir avantaj olarak vurgulanmıştır.","Anlayarak not almanın tarama testleri ve yazılı hazırlıklarında rahatlık sağlayacağını belirtmişlerdir."]},"beginTime":1773,"endTime":1815,"href":"/video/preview/17089670257672128761?parent-reqid=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-BAL&text=sinus+hd&t=1773&ask_summarization=1"},{"index":15,"title":"Ders Programı","list":{"type":"unordered","items":["Beşinci derste tanjant ve kotanjant fonksiyonları işlenecek ve bunlar bir çembere çizilen teğetlerle ilerleyecek.","Altıncı videodan itibaren öğretilen konularla ilgili işlemler yapılacak ve özdeşlikler, bölge, işaret, oran, trigonometrik oranlar gibi konular işlenecek.","Birinci üniteden sonra ikinci ünite olarak analitik geometri konusu gelecek ve bu konuyu Kenan Hoca anlatacak."]},"beginTime":1815,"endTime":1876,"href":"/video/preview/17089670257672128761?parent-reqid=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-BAL&text=sinus+hd&t=1815&ask_summarization=1"}],"linkTemplate":"/video/preview/17089670257672128761?parent-reqid=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-BAL&text=sinus+hd&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Trigonometri 4.Ders | Sinüs ve Cosinüs Fonksiyonları | 11.Sınıf Konu Anlatımı | Akademi Serisi","related_orig_text":"sinus 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işlevi dik üçgen'de Karşı dik kenar'ın Hipotenüs'e oranıdır. 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":"1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-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=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-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=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-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=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-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=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-BAL&text=sinus+hd&t=286&ask_summarization=1"}],"linkTemplate":"/video/preview/5443788018975714578?parent-reqid=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-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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boyunca; canlı yayınlar, konu anlatımları ve soru çözüm videolarıyla, tonguç yanında! Dersimiz #Matematik dersinin konularından \"Sinüs ve Kosinüs Teoremleri\". Hazırsan başlıyoruz! 😎...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2891134/6ead843ed1879e10270f51b7db541136/564x318_1"},"target":"_self","position":"2","reqid":"1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-BAL&text=videoid:5236752796704044973","teaser":[{"list":{"type":"unordered","items":["Bu video, Tonguç Akademi 10. sınıf kanalından bir matematik öğretmeninin sinüs ve kosinüs teoremlerini anlattığı eğitim içeriğidir.","Video, sinüs ve kosinüs teoremlerinin tanımı, formülleri, ispatları ve uygulamalarını kapsamaktadır. Öğretmen önce sinüs teoremini, ardından kosinüs teoremini detaylı şekilde açıklamakta, her iki teoremi de çeşitli örnek sorular üzerinden pekiştirmektedir. ","Video, TYT sınavına hazırlanan öğrenciler için sinüs ve kosinüs teoremlerini kapsamlı bir şekilde ele almakta, üçgenlerde kenar ve açı hesaplamaları için pratik yöntemler sunmaktadır. Ayrıca, sinüs teoreminin sinüs alan formülünden nasıl türetilebileceği ve kosinüs teoreminin dört adımda nasıl elde edildiği gibi detaylı ispatlar da içermektedir."]},"endTime":2479,"title":"10. 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=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-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=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-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=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-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=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-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=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-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=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-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=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-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=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-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=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-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=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-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=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-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=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-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=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-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=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-BAL&text=sinus+hd&t=2118&ask_summarization=1"}],"linkTemplate":"/video/preview/5236752796704044973?parent-reqid=1769366960265750-1372127323858153535-balancer-l7leveler-kubr-yp-vla-90-BAL&text=sinus+hd&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Sinüs ve Kosinüs Teoremleri | 10. 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Wenn er euch gefällt, lasst ein Abo/Like/Kommentar da. 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