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açı, toplam-fark ve dönüşüm formülleri) kullanılarak çeşitli problemlerin çözümleri gösterilmektedir. Öğretmen, sinüs, kosinüs ve tanjant fonksiyonlarının özellikleri, birim çember ve geometrik şekiller kullanılarak açıların değerlerinin bulunması gibi konuları ele almaktadır.","Video, Milli Eğitim Bakanlığı tarafından hazırlanan testin çözümlerini içermekte olup, 4. sorudan başlayarak 7. soruya kadar olan problemlerin çözümlerini kapsamaktadır. Ayrıca, Biruni'nin trigonometriyi kullanarak dağ yüksekliği ölçümü ve dünyanın çevresini hesaplama çalışmaları da anlatılmaktadır."]},"endTime":3241,"title":"12. 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kullanılarak sadeleştirme yapılmaktadır.","Sonuç olarak ifadenin değeri -1 olarak bulunmuştur."]},"beginTime":37,"endTime":284,"href":"/video/preview/12065455504577906678?parent-reqid=1774980508774145-1845896245624859037-balancer-l7leveler-kubr-yp-vla-231-BAL&text=Tim+J+Mat+-+Topic&t=37&ask_summarization=1"},{"index":2,"title":"İkinci Trigonometri Sorusu","list":{"type":"unordered","items":["İkinci soruda tanjant fonksiyonları kullanılarak x'in değeri bulunmaya çalışılmaktadır.","Tanjant 12, tanjant 49 ve tanjant x ifadeleri kullanılarak denklem çözülmektedir.","Sonuç olarak x = -61 veya 299 derece olarak bulunmuştur."]},"beginTime":284,"endTime":562,"href":"/video/preview/12065455504577906678?parent-reqid=1774980508774145-1845896245624859037-balancer-l7leveler-kubr-yp-vla-231-BAL&text=Tim+J+Mat+-+Topic&t=284&ask_summarization=1"},{"index":3,"title":"Üçüncü Trigonometri Sorusu","list":{"type":"unordered","items":["Üçüncü soruda sin²32 - sin²28 ifadesinin değeri sorulmaktadır.","Konuşmacı, matematik sorularının hemen çözülemediğinde hayal kırıklığına uğramamak gerektiğini vurgulamaktadır.","Soruda sinüs fonksiyonlarının kare farkı ve dönüşüm formülleri kullanılarak işlem yapılmaktadır."]},"beginTime":562,"endTime":758,"href":"/video/preview/12065455504577906678?parent-reqid=1774980508774145-1845896245624859037-balancer-l7leveler-kubr-yp-vla-231-BAL&text=Tim+J+Mat+-+Topic&t=562&ask_summarization=1"},{"index":4,"title":"Trigonometrik İfadelerin Çözümü","list":{"type":"unordered","items":["Kırmızı ifadede toplamlar var ve bu durumda kosinüslerde açıların farklarını, sinüslerde de toplamlarını yazmak gerekiyor.","İki sinüs 32 derece artı kosinüs 32 derece çarpı 2 ifadesi, 2 çarpı sinüs 62 derece çarpı kosinüs 2 derece şeklinde düzenleniyor.","İşlem sonucunda sinüs 4 derece çarpı kök 3 bölü 2 elde ediliyor ve bu ifade x çarpı kök 3 olarak yazılabilir."]},"beginTime":759,"endTime":909,"href":"/video/preview/12065455504577906678?parent-reqid=1774980508774145-1845896245624859037-balancer-l7leveler-kubr-yp-vla-231-BAL&text=Tim+J+Mat+-+Topic&t=759&ask_summarization=1"},{"index":5,"title":"Trigonometrik Denklemlerin Çözümü","list":{"type":"unordered","items":["x artı y = 60 derece verilmiş ve sin x artı cos y'nin karesi artı sin y artı cos x'in karesi soruluyor.","Kareler açıldığında sin²x + cos²x = 1 ve sin²y + cos²y = 1 olduğu görülüyor.","2(sin x cos y + sin y cos x) ifadesi sin(x+y) formülüne eşit olup, x+y = 60 derece olduğundan sin 60 = 1/2 olarak hesaplanıyor."]},"beginTime":909,"endTime":1064,"href":"/video/preview/12065455504577906678?parent-reqid=1774980508774145-1845896245624859037-balancer-l7leveler-kubr-yp-vla-231-BAL&text=Tim+J+Mat+-+Topic&t=909&ask_summarization=1"},{"index":6,"title":"Trigonometrik İfadelerin Değerlendirilmesi","list":{"type":"unordered","items":["1 - 8 sin²(π/8) cos²(π/8) ifadesi çözülüyor.","sin²x cos²x ifadesi sin 2x formülüne dönüştürülebiliyor ve π/8 = 22,5 derece olduğundan 2π/8 = 45 derece elde ediliyor.","İşlem sonucunda ifade 1 - (√2/2)² = 1 - 1/2 = 0 olarak bulunuyor."]},"beginTime":1064,"endTime":1197,"href":"/video/preview/12065455504577906678?parent-reqid=1774980508774145-1845896245624859037-balancer-l7leveler-kubr-yp-vla-231-BAL&text=Tim+J+Mat+-+Topic&t=1064&ask_summarization=1"},{"index":7,"title":"Kosinüs Farkı Formülünün Kullanımı","list":{"type":"unordered","items":["cos 72° - cos 36° ifadesi çözülüyor ve bu ifade eksi 2 sin 54° sin 18° formülüne dönüştürülüyor.","72° + 36° = 108° olduğu ve bu değer düzgün beşgenin iç açı ölçüsü olduğu belirtiliyor.","İşlem sonucunda ifade -1/2 olarak bulunuyor."]},"beginTime":1197,"endTime":1473,"href":"/video/preview/12065455504577906678?parent-reqid=1774980508774145-1845896245624859037-balancer-l7leveler-kubr-yp-vla-231-BAL&text=Tim+J+Mat+-+Topic&t=1197&ask_summarization=1"},{"index":8,"title":"Ark Tanjant İşlemleri","list":{"type":"unordered","items":["Ark tanjant x + ark tanjant (1-x) = ark tanjant (4/3) formülü inceleniyor.","Ark tanjant (4/3) hangi açının tanjant değeri olduğunu bulmak için tanjant formülü kullanılıyor.","Tanjant alfa + tanjant beta / (1 - tanjant alfa × tanjant beta) = 4/3 formülüyle x değeri bulunuyor."]},"beginTime":1486,"endTime":1653,"href":"/video/preview/12065455504577906678?parent-reqid=1774980508774145-1845896245624859037-balancer-l7leveler-kubr-yp-vla-231-BAL&text=Tim+J+Mat+-+Topic&t=1486&ask_summarization=1"},{"index":9,"title":"İkinci Dereceden Denklem Çözümü","list":{"type":"unordered","items":["4x² - 4x + 1 = 0 denklemi çözülüyor.","Denklem (2x - 1)² şeklinde factorize ediliyor.","Çözüm x = 1/2 olarak bulunuyor."]},"beginTime":1653,"endTime":1718,"href":"/video/preview/12065455504577906678?parent-reqid=1774980508774145-1845896245624859037-balancer-l7leveler-kubr-yp-vla-231-BAL&text=Tim+J+Mat+-+Topic&t=1653&ask_summarization=1"},{"index":10,"title":"Trigonometrik Denklem Çözümü","list":{"type":"unordered","items":["cos²(100°) - cos²(10°) / sin(70°) ifadesi çözülüyor.","cos(100°) = -sin(10°) olarak yazılıyor.","cos²(10°) - sin²(10°) = cos(20°) formülü kullanılarak sonucun -1 olduğu bulunuyor."]},"beginTime":1718,"endTime":1865,"href":"/video/preview/12065455504577906678?parent-reqid=1774980508774145-1845896245624859037-balancer-l7leveler-kubr-yp-vla-231-BAL&text=Tim+J+Mat+-+Topic&t=1718&ask_summarization=1"},{"index":11,"title":"Trigonometrik Problemin Çözümü","list":{"type":"unordered","items":["ABCD karesinde ED = 2k, DC = 5k, AD = 5k olarak belirleniyor.","Tanjant AEB (alfa) değeri soruluyor.","Alfa = 180° - (a + b) olarak ifade ediliyor ve tanjant formülü kullanılarak çözüm yapılıyor."]},"beginTime":1865,"endTime":2052,"href":"/video/preview/12065455504577906678?parent-reqid=1774980508774145-1845896245624859037-balancer-l7leveler-kubr-yp-vla-231-BAL&text=Tim+J+Mat+-+Topic&t=1865&ask_summarization=1"},{"index":12,"title":"Trigonometrik İşlemlerin Tamamlanması","list":{"type":"unordered","items":["Tanjant a = 5/2 ve tanjant b = 5/3 olarak belirleniyor.","(5/2 + 5/3) / (1 - 5/2 × 5/3) formülüyle hesaplama yapılıyor.","Sonuç 30/19 olarak bulunuyor."]},"beginTime":2052,"endTime":2126,"href":"/video/preview/12065455504577906678?parent-reqid=1774980508774145-1845896245624859037-balancer-l7leveler-kubr-yp-vla-231-BAL&text=Tim+J+Mat+-+Topic&t=2052&ask_summarization=1"},{"index":13,"title":"Biruni'nin Matematiksel Katkıları","list":{"type":"unordered","items":["Biruni, 1000-1200 yıllarında yaşamış ve trigonometriyi kullanarak dağların yüksekliğini ölçmüştür.","Trigonometri henüz yaygın olmadığı 9. yüzyıldan sonra Doğu'da trigonometriye ilerlemeler olmuştur.","Biruni, dağların yüksekliğini ölçtükten sonra dünyanın çevresini de ölçmüş ve oldukça başarılı sonuçlar elde etmiştir."]},"beginTime":2127,"endTime":2150,"href":"/video/preview/12065455504577906678?parent-reqid=1774980508774145-1845896245624859037-balancer-l7leveler-kubr-yp-vla-231-BAL&text=Tim+J+Mat+-+Topic&t=2127&ask_summarization=1"},{"index":14,"title":"Trigonometrik Denklem Çözümü","list":{"type":"unordered","items":["Verilen trigonometrik problemin çözümünde tanjant toplam fark formülü kullanılmaktadır.","Tanjant a-b değeri 1/5 olarak verilmiş ve bu değer kullanılarak x uzunluğu hesaplanacaktır.","Denklem çözüldüğünde x=4 değeri bulunmuştur."]},"beginTime":2150,"endTime":2513,"href":"/video/preview/12065455504577906678?parent-reqid=1774980508774145-1845896245624859037-balancer-l7leveler-kubr-yp-vla-231-BAL&text=Tim+J+Mat+-+Topic&t=2150&ask_summarization=1"},{"index":15,"title":"Sinüs ve Kosinüs Problemi","list":{"type":"unordered","items":["Sin 49 derece değeri m olarak verilmiş ve kos 16 derece değeri sorulmuştur.","Çözüm için 49 derecenin iki katı olan 98 derecenin 90+8 şeklinde yazılması ve kos 8 ile kos 16 arasındaki ilişki kurulması gerekmektedir.","Kos 49 değeri 1-m² karekökü olarak ifade edilmiş ve kos 8 değeri 2m√(1-m²) olarak bulunmuştur.","Sonuç olarak kos (-16) değeri 8m⁴-8m²+1 olarak hesaplanmıştır."]},"beginTime":2513,"endTime":2956,"href":"/video/preview/12065455504577906678?parent-reqid=1774980508774145-1845896245624859037-balancer-l7leveler-kubr-yp-vla-231-BAL&text=Tim+J+Mat+-+Topic&t=2513&ask_summarization=1"},{"index":16,"title":"Trigonometri Problemi Çözümü","list":{"type":"unordered","items":["Problemde alfa açısı π/2 ile 3π/2 arasında ve sin 2alfa = 24/25 verilmiş, kos alfa'nın değeri soruluyor.","Sin 2alfa verilmiş, kos alfa sorulduğu için yarım açı formülü kullanılacak.","24-25-7 üçgeni kullanılarak kos 2alfa = -7/25 bulunuyor."]},"beginTime":2964,"endTime":3075,"href":"/video/preview/12065455504577906678?parent-reqid=1774980508774145-1845896245624859037-balancer-l7leveler-kubr-yp-vla-231-BAL&text=Tim+J+Mat+-+Topic&t=2964&ask_summarization=1"},{"index":17,"title":"Kosinüs Formülü ve Denklem Çözümü","list":{"type":"unordered","items":["Kos 2alfa = 2kos²alfa - 1 formülü kullanılarak denklem kuruluyor.","-7/25 = 2kos²alfa - 1 denklemi çözülüyor ve kos²alfa = 16/25 bulunuyor.","Karekök alındığında kos alfa = 4/5 veya -4/5 oluyor, ancak verilen aralıkta kosinüs değeri negatif olduğu için -4/5 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