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Bir matematik öğretmeni tarafından sunulan ders, trigonometri konusunun 10. dersini kapsamaktadır.","Videoda sinüs, kosinüs, tanjant ve kotanjant fonksiyonlarının toplam fark formülleri detaylı olarak anlatılmaktadır. Öğretmen, bu formüllerin nasıl çalıştığını ve uygulandığını çeşitli örnekler üzerinden göstermekte, 146-152 sayfaları arasındaki konuları ele almaktadır. Ders boyunca 13. test ödevi verilmekte ve AYT sınavına hazırlanan öğrenciler için önemli stratejiler paylaşılmaktadır.","Video, trigonometrik fonksiyonların özellikleri, açı toplamı/farkı formülleri, bilinen açıların (30, 45, 60 derece) cinsinden diğer açıların hesaplanması ve geometrik şekillerde formüllerin kullanımı gibi konuları kapsamaktadır. Öğretmen, her soruyu adım adım çözerek uzun ve kısa çözüm yollarını göstermekte, özellikle tanjant formüllerinin ispatlarını ve uygulamalarını detaylı olarak açıklamaktadır."]},"endTime":5363,"title":"90 Gün Matematik Kampı: Trigonometri Toplam Fark Formülleri","beginTime":0}],"fullResult":[{"index":0,"title":"Matematik Kampı 35. Günü - Trigonometri 10. Ders","list":{"type":"unordered","items":["Gün matematik kampının 35. gününe geldik ve bugün toplam fark formülleri konusuna başlıyoruz.","Toplam fark formülleri, yarım açı formülleri, trigonometrik denklem ve eşitsizliklerle birlikte trigonometriyi noktalayacağız.","12. sınıf konularına da başlamış oluyoruz ve bu önemli bir ders olacak."]},"beginTime":0,"endTime":25,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=0&ask_summarization=1"},{"index":1,"title":"Kamp Programı ve Ders Planı","list":{"type":"unordered","items":["35. günde iki video izleyeceğiz ve bu videolar çok yoğun olacak.","35. günde trigonometri 10. ve 11. dersler işlenecek, 10. ders bu videoda, 11. ders sonraki videoda.","36. günde ise yarım açı formülleri konusuna 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Açılımları","list":{"type":"unordered","items":["Sinüs ve kosinüs fonksiyonlarının açılımları inceleniyor.","Sinüs x artı y'nin açılımı sinüs x artı y eşittir bir, çünkü doksan derecenin sinüs değeri bir'dir.","Kotanjant 90 derecenin değeri sıfırdır."]},"beginTime":1635,"endTime":1684,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=1635&ask_summarization=1"},{"index":10,"title":"Trigonometrik Denklemlerin Çözümü","list":{"type":"unordered","items":["Tanjant a'yı verilmiş, kotanjant b'yi verilmiş ifadelerin eşitini bulma problemi ele alınıyor.","Bilinen açılar yerine trigonometrik değerler kullanılarak sinüs a artı b açılımı yapılarak soru çözülüyor.","Sonuç olarak sinüs a çarpı kosinüs b ifadesi bulunarak cevap 4/5√2 olarak hesaplanıyor."]},"beginTime":1684,"endTime":1845,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=1684&ask_summarization=1"},{"index":11,"title":"Üçgenin Açıları ve Trigonometrik İşlemler","list":{"type":"unordered","items":["ABC üçgeninde açıların toplamının 180 derece olduğu belirtiliyor.","C açısının kotanjantı, 180 eksi (a artı b) açısının kotanjantı olarak ifade ediliyor.","Kotanjantın ikinci bölgede işareti eksi olduğu için kotanjant c, eksi kotanjant (a artı b) olarak bulunuyor."]},"beginTime":1845,"endTime":1930,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=1845&ask_summarization=1"},{"index":12,"title":"Trigonometrik Fonksiyonların Değerleri","list":{"type":"unordered","items":["Tanjant a artı b formülü kullanılarak tanjant a artı b değeri 9/7 olarak hesaplanıyor.","Kotanjant a artı b değeri 7/9 olarak bulunuyor.","Sonuç olarak eksi 7/9 olarak cevap bulunuyor."]},"beginTime":1930,"endTime":2048,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=1930&ask_summarization=1"},{"index":13,"title":"Trigonometrik Değerlerin İlişkisi","list":{"type":"unordered","items":["Kotanjant 70 derecenin ve tanjant 75 derecenin değerleri verilmiş.","Tanjant 35 derecenin bu değerler cinsinden eşiti bulunması isteniyor."]},"beginTime":2048,"endTime":2069,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=2048&ask_summarization=1"},{"index":14,"title":"Trigonometrik Fonksiyonlar ve Toplam Fark Formülleri","list":{"type":"unordered","items":["Tanjant 35 derecenin tanjant 20 derece ve kotanjant 15 derece cinsinden değerini bulmak için toplam fark formülü kullanılır.","Tanjant 75 derecenin kotanjant 15 dereceye eşit olduğu ve tanjant 20 derecenin a, kotanjant 15 derecenin ise 1/b şeklinde ifade edildiği gösterilir.","Toplam fark formülü kullanılarak tanjant 35 derecenin a ve b cinsinden değeri (ab+1)/(b-a) olarak hesaplanır."]},"beginTime":2076,"endTime":2198,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=2076&ask_summarization=1"},{"index":15,"title":"Çocukluk Anıları","list":{"type":"unordered","items":["Konuşmacı, çocukluğunda sokakta kart oyunları oynadıklarını ve mahallede futbolcu kartları topladıklarını anlatır.","Tribine girip oyun oynamak yerine sokakta oynamak daha keyifli olduğunu belirtir.","Teknoloji çağında büyümek istediğini, 10 yaşındayken PlayStation ile GTA 5 oynamak istediğini ifade eder."]},"beginTime":2198,"endTime":2309,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=2198&ask_summarization=1"},{"index":16,"title":"Trigonometrik Denklemler","list":{"type":"unordered","items":["Tanjant 20 derecenin a cinsinden eşitini bulmak için kotanjant 55 derecenin tanjant 35 dereceye eşit olduğu gösterilir.","Tanjant 70 derecenin tanjant 35+35 formülü kullanılarak (2a)/(1-a²) olarak hesaplanır.","Kotanjant 70 derecenin tanjant 70 derecenin takla atılmış hali olarak (1-a²)/(2a) olarak bulunur."]},"beginTime":2309,"endTime":2436,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=2309&ask_summarization=1"},{"index":17,"title":"Trigonometrik İfadelerin Eşitleri","list":{"type":"unordered","items":["Sinüs 20+cos 20+tan 50×sin 40 ifadesinin eşitini bulmak için tanjant 50 derecenin sinüs 50/cos 50 şeklinde yazılması önerilir.","Payda eşitleme yöntemi kullanılarak ifade sin 70/cos 50 olarak sadeleştirilir.","Kök 3 ifadesinin trigonometrik sorularda tanjant 60 dereceye (sin 60/cos 60) çevrilmesiyle kullanılabileceği belirtilir."]},"beginTime":2436,"endTime":2636,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=2436&ask_summarization=1"},{"index":18,"title":"Trigonometrik İfadelerin Sadeleştirilmesi","list":{"type":"unordered","items":["Sin 20+√3×cos 20/cos 60×sin 60 ifadesinde kök 3 yerine tanjant 60 derece (sin 60/cos 60) yazılır.","Payda eşitleme yöntemi kullanılarak ifade sin 80/cos 60 olarak sadeleştirilir.","Sonuç olarak ifadenin 2 olarak bulunması gösterilir."]},"beginTime":2636,"endTime":2721,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=2636&ask_summarization=1"},{"index":19,"title":"Trigonometrik Denklem Çözümü","list":{"type":"unordered","items":["Trigonometrik denklemi çözmek için sinüs x+30'ı açarak sinüs x kosinüs 30 + kosinüs x sinüs 30 şeklinde ifade ediyoruz.","İçler dışlar çarpımı yaparak denklemi sadeleştiriyoruz ve tanjant x'i bulmak için sinüs x'i kosinüs x'e bölüyoruz.","Sonuç olarak tanjant x'in değeri -√3 olarak bulunuyor."]},"beginTime":2725,"endTime":2908,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=2725&ask_summarization=1"},{"index":20,"title":"Kısa Yöntem ve Öneriler","list":{"type":"unordered","items":["Kısa yöntem olarak x'e 120 derece değerini vererek denklemi kontrol edebiliriz, çünkü sinüs 150/2 = 1/2 olur.","AYT sınavında kısa yollar kullanılabilir ancak uzun yolları da bilmek önemlidir çünkü ÖSYM sadece kısa yollardan çözülebilecek soruları çok fazla çıkarmaz."]},"beginTime":2908,"endTime":3059,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=2908&ask_summarization=1"},{"index":21,"title":"Üçgen Problemi Çözümü","list":{"type":"unordered","items":["Dar açılı bir ABC üçgeninde verilen denklemleri kare alarak sinüs A+B = 1/2 elde ediyoruz.","Sinüs 1/2 olduğunda açı 30 veya 150 derece olabilir, ancak dar açılı üçgen için A+B = 150 derece olmalı.","Bu durumda C açısının ölçüsü 30 derece olarak bulunuyor."]},"beginTime":3059,"endTime":3288,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=3059&ask_summarization=1"},{"index":22,"title":"Karmaşık Trigonometrik Denklem","list":{"type":"unordered","items":["A ve B dar açı olmak üzere verilen denklemlerle sinüs 4A+5B-3C değerini bulmaya çalışıyoruz.","Denklemleri manipüle ederek sinüs 4A+5B-3C = sinüs 2A+4B ilişkisini kuruyoruz.","Sinüs toplam farkı formülü kullanarak sinüs 2A+4B'yi hesaplayıp sonucu 117/125 olarak buluyoruz."]},"beginTime":3288,"endTime":3531,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=3288&ask_summarization=1"},{"index":23,"title":"Trigonometri Problemi Çözümü","list":{"type":"unordered","items":["Dar açılı bir üçgende sinüs ve kosinüs değerleri kullanılarak kosinüs M açısının değeri bulunuyor.","Üçgenin iç açıları toplamı 180 derece olduğundan, M+R+T=180 ve M+R=180-T ilişkisi kuruluyor.","Sinüs açılımı kullanılarak sinüs M açısının 1/√6 olduğu ve kotanjant M açısının √5 olduğu bulunuyor."]},"beginTime":3536,"endTime":3679,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=3536&ask_summarization=1"},{"index":24,"title":"Trigonometrik İşlem Çözümü","list":{"type":"unordered","items":["Tanjant 50 - tanjant 40 bölü tanjant 10 işleminin sonucu hesaplanıyor.","Tanjant değerleri sinüs ve kosinüs oranları olarak yazılır ve payda eşitlenerek işlem yapılır.","Sinüs açılımı kullanılarak sinüs 10 ve sinüs 80 değerleri bulunarak sonuç 2 olarak hesaplanıyor."]},"beginTime":3679,"endTime":3888,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=3679&ask_summarization=1"},{"index":25,"title":"Şekilli Trigonometri Problemi","list":{"type":"unordered","items":["Sekiz eş dikdörtgenden oluşan bir şekildedir ve B açısının tanjantı soruluyor.","Şekildeki üçgenler incelenerek tanjant (x+y) değeri 4/5 olarak bulunuyor.","Tanjant y değeri 3/11 olarak hesaplanıyor ve tanjant (x+y) açılımı kullanılarak tanjant x değeri bulunmaya çalışılıyor."]},"beginTime":3888,"endTime":4087,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=3888&ask_summarization=1"},{"index":26,"title":"Trigonometrik Denklemin Çözümü","list":{"type":"unordered","items":["Bir trigonometrik denklemde payda eşitliği ve içler dışlar çarpımı kullanılarak a değeri bulunuyor.","İşlemler sonucunda tanjant a değeri 29/67 olarak hesaplanıyor."]},"beginTime":4104,"endTime":4145,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=4104&ask_summarization=1"},{"index":27,"title":"Trigonometrik Not ve Uygulaması","list":{"type":"unordered","items":["a·sinx ± b·cosx = c ifadesinde a² + b² = c² olduğunda, her iki tarafı c'ye bölerek toplam fark formülleri kullanılabilir.","Örnek olarak √3·sinx + 2·cosx = √7 denklemi verilmiş ve √3² + 2² = (√7)² olduğu için formül kullanılabilir.","Denklemdeki katsayılar Pisagor teoremini sağladığı için, bunlar bir üçgenin kenarlarını oluşturabilir."]},"beginTime":4145,"endTime":4311,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=4145&ask_summarization=1"},{"index":28,"title":"Trigonometrik Çözümün Tamamlanması","list":{"type":"unordered","items":["Denklem sinx + cosx = 1 formuna dönüştürüldüğünde, kosinüs fark açılımı kullanılarak x - a = 0 bulunuyor.","x = a olduğu için sinx = sin(a) = √3/√7 olarak hesaplanıyor."]},"beginTime":4311,"endTime":4370,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=4311&ask_summarization=1"},{"index":29,"title":"Ek Özellikler","list":{"type":"unordered","items":["Video ekstra özellikler içeren bir sayfaya geçiliyor.","Bu özellikler önceki yıllarda yokken, bu sene eklenen önemli trigonometrik özelliklerdir.","Bu özellikler zor sorularda ara ifadeler olarak kullanılabilir ve sınavlarda sorulma ihtimali olan konulardır."]},"beginTime":4370,"endTime":4416,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=4370&ask_summarization=1"},{"index":30,"title":"Trigonometrik Özelliğin İspatı","list":{"type":"unordered","items":["Tanjant a + tanjant b = 1 formülünden yola çıkarak, (1 + tanjant a) × (1 + tanjant b) = 2 eşitliği ispatlanmıştır.","Bu eşitlik, a + b = 45 derece olduğunda geçerlidir.","Örneğin, tanjant 12 + tanjant 33 = 2 ve tanjant 19 + tanjant 26 = 2 gibi örnekler verilmiştir."]},"beginTime":4419,"endTime":4552,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=4419&ask_summarization=1"},{"index":31,"title":"Trigonometrik Problemin Çözümü","list":{"type":"unordered","items":["ABC dar açılar olmak üzere, tanjant a, tanjant b ve tanjant c değerleri verilmiş, kosinüs c sorulmuştur.","Tanjant (a+b+c) formülü kullanılarak tanjant (a+b) = -1 bulunmuştur.","Tanjant c = 1/2 olarak hesaplanarak, kosinüs c = 2√5/5 olarak bulunmuştur."]},"beginTime":4552,"endTime":4782,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=4552&ask_summarization=1"},{"index":32,"title":"Trigonometrik İfadelerin Değerlendirilmesi","list":{"type":"unordered","items":["Tanjant 24 + tanjant 16 / tanjant 40 + tanjant 24 - tanjant 16 / tanjant 8 ifadesinin değeri hesaplanmıştır.","Tanjant toplam-fark formülleri kullanılarak ifade sadeleştirilmiştir.","Sonuç olarak ifadenin değeri 2 olarak bulunmuştur."]},"beginTime":4782,"endTime":4923,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=4782&ask_summarization=1"},{"index":33,"title":"Trigonometrik Bağıntılar","list":{"type":"unordered","items":["Ayırt edici bir not olarak, trigonometrik denklemlerde sıkça kullanılan bir + tanjant x / 1 - tanjant x = tanjant (x + 45) bağıntısı verilmiştir.","Benzer şekilde 1 - tanjant x / 1 + tanjant x = tanjant (45 - x) bağıntısı da açıklanmıştır.","Bu bağıntılar, trigonometrik denklemlerde sıkça kullanılır ve önemli notlar olarak belirtilmiştir."]},"beginTime":4923,"endTime":5080,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=4923&ask_summarization=1"},{"index":34,"title":"Trigonometrik İşlemler","list":{"type":"unordered","items":["Kök üç değerlerinde tanjant 60 derece, sinüs 60 derece bölü kosinüs 60 derece olarak değerlendirilir.","Soruda hem pay hem payda kısmında trigonometrik değerler bulunmaktadır.","Sinüs 60, sinüs 20, kosinüs 60 ve kosinüs 20 değerleri kullanılarak payda eşitleme yapılır."]},"beginTime":5087,"endTime":5177,"href":"/video/preview/5247346249405727320?parent-reqid=1765379307334468-6173791626720174004-balancer-l7leveler-kubr-yp-sas-108-BAL&text=%F0%9F%92%9FMETADtv&t=5087&ask_summarization=1"},{"index":35,"title":"Trigonometrik Denklemlerin Çözümü","list":{"type":"unordered","items":["Kosinüs açılımı eksi değer alırken, sinüs açılımı ise eksi devam eder.","Kos 40 ve sin 50 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