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Öğretmen, 126'dan 142'ye kadar olan soruları çözmekte ve sonraki derste 13 sorunun çözüleceği bilgisini vermektedir."]},"endTime":1873,"title":"AYT Matematik Kampı: Trigonometri II - Toplam Fark Formülleri","beginTime":0}],"fullResult":[{"index":0,"title":"AYT Matematik Kampı ve Trigonometri","list":{"type":"unordered","items":["AYT matematik kampının 34. gününde trigonometrinin sonuna doğru ilerleniyor.","Trigonometri 2 bölümünde toplam fark formülleri, yarım açı formülleri ve trigonometrik denklemler konuları işleniyor.","Trigonometrik denklemler bölümünde en az iki soru çıkıyor."]},"beginTime":0,"endTime":48,"href":"/video/preview/13860495908431618017?parent-reqid=1769446489348480-11275240215616461642-balancer-l7leveler-kubr-yp-sas-25-BAL&text=Full+Auto+Mathematics&t=0&ask_summarization=1"},{"index":1,"title":"Ders Planı ve Önemli Bilgiler","list":{"type":"unordered","items":["Öğrencilerin sosyal medyadan uzak durup sadece ders konularına odaklanmaları isteniyor.","16. ve 17. derslerde trigonometrik toplam fark formülleri işlenecek.","GPT soru bankasındaki 13. test (152. sayfa) çözülmeli ve en az iki kitap çalışılmalı."]},"beginTime":48,"endTime":129,"href":"/video/preview/13860495908431618017?parent-reqid=1769446489348480-11275240215616461642-balancer-l7leveler-kubr-yp-sas-25-BAL&text=Full+Auto+Mathematics&t=48&ask_summarization=1"},{"index":2,"title":"Toplam Fark Formülleri","list":{"type":"unordered","items":["Toplam fark formülleri, yarım açı formüllerinin aynısıdır, sadece iki açıya eşit seçilir.","İki açının toplamı veya farkı biçiminde yazılan açıların trigonometrik oranları bulunurken kullanılan formüllere toplam fark formülleri denir.","Sinüsün toplam fark formüllerinde \"isimler ters, işaret aynı\" kuralı uygulanır."]},"beginTime":129,"endTime":270,"href":"/video/preview/13860495908431618017?parent-reqid=1769446489348480-11275240215616461642-balancer-l7leveler-kubr-yp-sas-25-BAL&text=Full+Auto+Mathematics&t=129&ask_summarization=1"},{"index":3,"title":"Sinüsün Toplam ve Fark Formülleri","list":{"type":"unordered","items":["Sinüsün toplam formülü: sin(a+b) = sin(a)cos(b) + cos(a)sin(b)","Sinüsün fark formülü: sin(a-b) = sin(a)cos(b) - cos(a)sin(b)","Sinüsün formüllerinde ilk açının sinüsü, ikinci açının kosinüsü ve ikinci açının sinüsü, ilk açının kosinüsü şeklinde yazılır."]},"beginTime":270,"endTime":380,"href":"/video/preview/13860495908431618017?parent-reqid=1769446489348480-11275240215616461642-balancer-l7leveler-kubr-yp-sas-25-BAL&text=Full+Auto+Mathematics&t=270&ask_summarization=1"},{"index":4,"title":"Örnek Uygulama","list":{"type":"unordered","items":["Sinüs 105 derecenin değeri hesaplanırken, 105 derecenin 60 derecenin ve 45 derecenin toplamı olduğu kullanılır.","Sinüs 105 = sin(60°+45°) = sin(60°)cos(45°) + cos(60°)sin(45°) formülü uygulanır.","Sinüs 60° = √3/2, sinüs 45° = √2/2 değerleri kullanılarak sinüs 105 = (√3/2)cos(45°) + cos(60°)sin(45°) = (√3/2)×(√2/2) + (√2/2)×(√3/2) = √6/4 = √3/2 olarak bulunur."]},"beginTime":380,"endTime":439,"href":"/video/preview/13860495908431618017?parent-reqid=1769446489348480-11275240215616461642-balancer-l7leveler-kubr-yp-sas-25-BAL&text=Full+Auto+Mathematics&t=380&ask_summarization=1"},{"index":5,"title":"Kosinüs Formülleri","list":{"type":"unordered","items":["Kosinüs formüllerinde isimler aynı gelirken, aradaki işaret ters olur.","Kosinüs formülleri hep \"koskos\" ile başlar, \"sinsin\" ile başlarsanız işareti kaçırırsınız.","Kosinüs toplam formülü: cos(a+b) = cos(a)cos(b) - sin(a)sin(b)","Kosinüs fark formülü: cos(a-b) = cos(a)cos(b) + sin(a)sin(b)"]},"beginTime":441,"endTime":544,"href":"/video/preview/13860495908431618017?parent-reqid=1769446489348480-11275240215616461642-balancer-l7leveler-kubr-yp-sas-25-BAL&text=Full+Auto+Mathematics&t=441&ask_summarization=1"},{"index":6,"title":"Kosinüs Formüllerinin Uygulanması","list":{"type":"unordered","items":["Kosinüs 75° gibi bir değer sorulduğunda, 75°'yi 45° ile 30°'un toplamı olarak yazıp kosinüs toplam formülünü uygulayabilirsiniz.","Kotanjant formülünü ezberlemek yerine, tanjant formülünü bulup takla attırarak kotanjant değerini bulabilirsiniz.","Tanjant toplam formülü: tan(a+b) = (tan(a) + tan(b)) / (1 - tan(a)tan(b))","Tanjant formülünde işaretler: tanjantta artı ile başlar, eksiyle devam eder."]},"beginTime":544,"endTime":649,"href":"/video/preview/13860495908431618017?parent-reqid=1769446489348480-11275240215616461642-balancer-l7leveler-kubr-yp-sas-25-BAL&text=Full+Auto+Mathematics&t=544&ask_summarization=1"},{"index":7,"title":"Trigonometrik Toplam ve Fark Formülleri","list":{"type":"unordered","items":["Tanjant toplam formülü \"tan tan van tan tan\" şeklindedir; işaret artı ise artı ile başlar, eksi ise eksi ile devam eder.","Tanjant fark formülü \"tan tan van tan tan\" şeklindedir; işaret eksi ise alttaki artı işaretine dönüşür.","Kotanjant, tanjantın tersi olduğundan, tanjant formülü bilindiğinde kotanjant formülü takla atılarak bulunabilir."]},"beginTime":664,"endTime":736,"href":"/video/preview/13860495908431618017?parent-reqid=1769446489348480-11275240215616461642-balancer-l7leveler-kubr-yp-sas-25-BAL&text=Full+Auto+Mathematics&t=664&ask_summarization=1"},{"index":8,"title":"Sinüs Toplam ve Fark Formülleri","list":{"type":"unordered","items":["Sinüs toplam formülü \"sinüs isimler ters, işaret aradakinin aynısı\" şeklindedir.","Sinüs fark formülü \"sinüs isimler ters, işaret aradakinin tam tersi\" şeklindedir.","Trigonometrik oranlar bilinen iki açının toplamı veya farkı olarak yazılabilir."]},"beginTime":736,"endTime":736,"href":"/video/preview/13860495908431618017?parent-reqid=1769446489348480-11275240215616461642-balancer-l7leveler-kubr-yp-sas-25-BAL&text=Full+Auto+Mathematics&t=736&ask_summarization=1"},{"index":9,"title":"Tanjant ve Kotanjant Hesaplamaları","list":{"type":"unordered","items":["Tanjant 15° = tanjant (60° - 45°) = (√3) / (1) = √3 olarak hesaplanır.","Kotanjant 15° = 1 / tanjant 15° = (1 + √3) / (√3 - 1) olarak hesaplanır.","Tanjant 75° = tanjant (45° + 30°) = (1 + 1/√3) / (1 - 1/√3) = (√3 + 1) / (√3 - 1) olarak hesaplanır."]},"beginTime":990,"endTime":1171,"href":"/video/preview/13860495908431618017?parent-reqid=1769446489348480-11275240215616461642-balancer-l7leveler-kubr-yp-sas-25-BAL&text=Full+Auto+Mathematics&t=990&ask_summarization=1"},{"index":10,"title":"Klasik Soruların Çözümü","list":{"type":"unordered","items":["Dersin sonunda klasik soruların çözümüne geçilecek ve 126'dan 142'ye kadar olan 16 soru çözülecek.","İlk soruda sinüs x ve kosinüs y değerleri verilmiş, sinüs x+y hesaplanacak.","Sinüs toplam formülü kullanılarak sinüs x+y = sinüs 40° × kosinüs y + sinüs y × kosinüs x şeklinde ifade edilir."]},"beginTime":1175,"endTime":1230,"href":"/video/preview/13860495908431618017?parent-reqid=1769446489348480-11275240215616461642-balancer-l7leveler-kubr-yp-sas-25-BAL&text=Full+Auto+Mathematics&t=1175&ask_summarization=1"},{"index":11,"title":"Dik Üçgenlerle Hesaplama","list":{"type":"unordered","items":["Sinüs x = 1/3 ve kosinüs y = √3/3 verilmiş, sinüs y ve kosinüs x değerleri dik üçgenler çizilerek bulunur.","Sinüs x için dik üçgende karşı kenar 1, hipotenüs 3 olduğundan komşu kenar 2√2 olarak hesaplanır.","Sinüs y için dik üçgende komşu kenar √3, hipotenüs 3 olduğundan karşı kenar √6 olarak hesaplanır."]},"beginTime":1230,"endTime":1334,"href":"/video/preview/13860495908431618017?parent-reqid=1769446489348480-11275240215616461642-balancer-l7leveler-kubr-yp-sas-25-BAL&text=Full+Auto+Mathematics&t=1230&ask_summarization=1"},{"index":12,"title":"Sonuç Hesaplama","list":{"type":"unordered","items":["Sinüs x = 1/3, sinüs y = √6/3 olarak bulunur ve sinüs x+y = (1/3 + √6/3) × (1/3 - √6/3) şeklinde hesaplanır.","İşlemler sonucunda sinüs x+y = 5√3/9 olarak bulunur ve sorunun doğru cevabı E şıkkıdır."]},"beginTime":1334,"endTime":1374,"href":"/video/preview/13860495908431618017?parent-reqid=1769446489348480-11275240215616461642-balancer-l7leveler-kubr-yp-sas-25-BAL&text=Full+Auto+Mathematics&t=1334&ask_summarization=1"},{"index":13,"title":"İkinci Soru Çözümü","list":{"type":"unordered","items":["İkinci soruda sinüs ve kosinüs değerleri verilmiş, sinüs 65° + sinüs 25° + sinüs 25° + sinüs 65° ifadesi hesaplanacak.","Açılar aynı durumda olduğu için sinüs toplam formülü kullanılır ve sinüs 90° = 1 olarak bulunur.","İkinci ifadede sinüs 57° - sinüs 27° - sinüs 27° - sinüs 33° ifadesi hesaplanır, 57° açısı 90° - 33° = 57° olarak değiştirilerek sinüs 57° = kosinüs 57° olarak yazılır."]},"beginTime":1374,"endTime":1477,"href":"/video/preview/13860495908431618017?parent-reqid=1769446489348480-11275240215616461642-balancer-l7leveler-kubr-yp-sas-25-BAL&text=Full+Auto+Mathematics&t=1374&ask_summarization=1"},{"index":14,"title":"Sonuç Hesaplama","list":{"type":"unordered","items":["Sinüs 57° - sinüs 27° - sinüs 27° - sinüs 33° ifadesi sinüs toplam formülü kullanılarak hesaplanır.","Sinüs 57° = kosinüs 57° olduğundan sinüs 57° - sinüs 27° = -sinüs 27° olarak yazılır.","İşlemler sonucunda sinüs 57° - sinüs 27° = 1/2 olarak bulunur ve sorunun doğru cevabı 2'dir."]},"beginTime":1477,"endTime":1507,"href":"/video/preview/13860495908431618017?parent-reqid=1769446489348480-11275240215616461642-balancer-l7leveler-kubr-yp-sas-25-BAL&text=Full+Auto+Mathematics&t=1477&ask_summarization=1"},{"index":15,"title":"Trigonometrik Formüllerin Kullanımı","list":{"type":"unordered","items":["Trigonometrik ifadelerde açıların aynı olması durumunda formüller kullanılabilir.","Kosinüs formülünde isimler aynı gelirken işaret ters gelir, sinüs formülünde ise isimler ters gelirken işaret aynı gelir.","Trigonometrik ifadelerde açıların aynı olması durumunda formüller kullanılarak değerler bulunabilir."]},"beginTime":1508,"endTime":1577,"href":"/video/preview/13860495908431618017?parent-reqid=1769446489348480-11275240215616461642-balancer-l7leveler-kubr-yp-sas-25-BAL&text=Full+Auto+Mathematics&t=1508&ask_summarization=1"},{"index":16,"title":"Trigonometrik İfadelerin Çözümü","list":{"type":"unordered","items":["Trigonometrik ifadelerde kare alma işlemi yapılarak sin²21 + 2sin21cos39 + cos²39 şeklinde açılır.","Sin²39 + cos²39 = 1 ve sin21cos39 = sin39cos21 formülleri kullanılarak ifade sadeleştirilir.","Sin39cos21 = sin60 = √3/2 olduğundan, ifadenin değeri 2 + √3 olarak bulunur."]},"beginTime":1577,"endTime":1712,"href":"/video/preview/13860495908431618017?parent-reqid=1769446489348480-11275240215616461642-balancer-l7leveler-kubr-yp-sas-25-BAL&text=Full+Auto+Mathematics&t=1577&ask_summarization=1"},{"index":17,"title":"İkinci Trigonometrik İfadenin Çözümü","list":{"type":"unordered","items":["Trigonometrik ifadede sin74cos12 + cos74sin12 şeklinde açılır ve sinüs formülü kullanılarak sin62 olarak sadeleştirilir.","Kosinüs formülünde kosinüs başta olmalı ve aradaki işaretin tam tersi gelir.","Kos118 = -cos62 olduğundan, ifade -tan62 olarak bulunur."]},"beginTime":1712,"endTime":1855,"href":"/video/preview/13860495908431618017?parent-reqid=1769446489348480-11275240215616461642-balancer-l7leveler-kubr-yp-sas-25-BAL&text=Full+Auto+Mathematics&t=1712&ask_summarization=1"},{"index":18,"title":"Dersin Sonu","list":{"type":"unordered","items":["Toplam 13 soru çözülmüş ve her birini ikişer dakikada çözersek toplam 26 dakika sürmüş.","Sonraki derste her bir soru ikişer dakikada çözülecek ve video süreleri aşağı yukarı eşit olacak."]},"beginTime":1855,"endTime":1872,"href":"/video/preview/13860495908431618017?parent-reqid=1769446489348480-11275240215616461642-balancer-l7leveler-kubr-yp-sas-25-BAL&text=Full+Auto+Mathematics&t=1855&ask_summarization=1"}],"linkTemplate":"/video/preview/13860495908431618017?parent-reqid=1769446489348480-11275240215616461642-balancer-l7leveler-kubr-yp-sas-25-BAL&text=Full+Auto+Mathematics&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"80 Günde AYT Matematik Kampı | 34. 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