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Öğretmen, sinüs, kosinüs, tanjant ve kotanjant fonksiyonlarının toplam ve fark formüllerini teorik olarak anlatıp, ardından çeşitli örnekler üzerinden uygulamaları göstermektedir. Video, formüllerin ezberlenmesi için pratik yöntemler sunmakta ve soru çözümleriyle konuyu pekiştirmektedir.","Videoda ayrıca yarım açı formüllerinin toplam fark formülleriyle ilişkisi, 90 dereceye tamamlayan açılar arasındaki ilişki ve dik üçgenlerde Pisagor bağıntısının kullanımı gibi konular da işlenmektedir. 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=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++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=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++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=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++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=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++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=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++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=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++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=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++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=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++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=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++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=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++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=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++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=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++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=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++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=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++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=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++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=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++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=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++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=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++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=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++Mathematics&t=1855&ask_summarization=1"}],"linkTemplate":"/video/preview/13860495908431618017?parent-reqid=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++Mathematics&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"80 Günde AYT Matematik Kampı | 34. 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We are starting our 80-day AYT Mathematics Camp, which we have updated to provide you with the most...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3174656/560ee85db5e6aa4756cb130947a1caaa/564x318_1"},"target":"_self","position":"18","reqid":"1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=videoid:11095231301459517085","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik öğretmeninin trigonometri konusunu anlattığı kapsamlı bir eğitim içeriğidir. Öğretmen, devlette çalışan ve kendi eğitim kanalını kurmuş bir öğretmen olarak kendini tanıtmaktadır.","Videoda trigonometrik fonksiyonlar (sinüs, kosinüs, tanjant, kotanjant) ve bunların toplam-fark formülleri detaylı şekilde ele alınmaktadır. Öğretmen, 130. sorudan başlayarak çeşitli trigonometrik soruları adım adım çözmekte, dik üçgenler çizerek trigonometrik değerleri hesaplamakta ve formülleri uygulamaktadır. Video, trigonometri konusunda pratik yapmak isteyen öğrenciler için faydalı bir kaynak niteliğindedir.","Öğretmen, bir sonraki derste şekiller ve yarım açı formülleri konularını ele alacağını belirtmektedir. Ayrıca, trigonometrik denklemlerde yarım açı formüllerinin her yıl bir soru olarak sorulduğu vurgulanmaktadır. Video, \"iyi ki\" dediğiniz şey sayısı, \"keşke\" dediğiniz şey sayısından fazlaysa başardınız\" mesajıyla motivasyon vererek başlamakta ve toplam fark formüllerine geçiş yapmaktadır."]},"endTime":2339,"title":"Trigonometri Dersi: Toplam-Fark Formülleri ve Çözümlü Sorular","beginTime":0}],"fullResult":[{"index":0,"title":"Kanalın Başlangıcı ve Zorluklar","list":{"type":"unordered","items":["Konuşmacı, kanalında \"değerli öğrencilerim, sevgili arkadaşlarım\" ifadesini çok sık kullandığını belirtiyor.","İlk başlangıcında bir kurumda çalışırken haksızlıklar yaşadığını ve bu nedenle ayrıldığını anlatıyor.","Yayınevleri onu bir yayıncı yapmak zorunda bıraktığını ve bu durumun öğretmenler için sıkıntılı olduğunu ifade ediyor."]},"beginTime":0,"endTime":62,"href":"/video/preview/11095231301459517085?parent-reqid=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++Mathematics&t=0&ask_summarization=1"},{"index":1,"title":"Çalışma Süreci ve Fedakarlık","list":{"type":"unordered","items":["Gece yazıp sabah video çektiğini, üniversite sınavı kazanma gibi başarılarla karşılaştığını anlatıyor.","Devlette çalışırken gündüz okul işleri, gece saat 11'den sonra video çektiğini ve bu süreçlerin çok yorucu olduğunu belirtiyor.","Hayatının beş yılını bu işe harcadığını, tatil yapamadığını ve birçok şeyi kaybettiğini, ancak bunun güzel olduğunu düşünüyor."]},"beginTime":62,"endTime":125,"href":"/video/preview/11095231301459517085?parent-reqid=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++Mathematics&t=62&ask_summarization=1"},{"index":2,"title":"Başarı ve Pişmanlık","list":{"type":"unordered","items":["Bazı şeyleri yapmak için fedakarlık yapmanın gerekliliğini vurguluyor.","İleride pişmanlık yaşayacağından emin olmadığını, ancak \"iyi ki\" diyebileceği şeyin \"keşke\" diyebileceğinden fazla olması gerektiğini belirtiyor.","Bu durumun başarı olduğunu ve bunun için mücadele edilmesi gerektiğini söylüyor."]},"beginTime":125,"endTime":175,"href":"/video/preview/11095231301459517085?parent-reqid=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++Mathematics&t=125&ask_summarization=1"},{"index":3,"title":"Trigonometri Soru Çözümü","list":{"type":"unordered","items":["Öğretmen, kosinüs fark formülü kullanarak trigonometri soruları çözeceğini belirtiyor.","İlk soruda, 0 ile 1/2 arasında x ve y açıları için kosinüs x - y değerini bulmak için dik üçgenler çiziliyor.","Tanjant ve kotanjant değerleri kullanılarak dik üçgenler çizilerek kosinüs ve sinüs değerleri hesaplanıyor."]},"beginTime":180,"endTime":207,"href":"/video/preview/11095231301459517085?parent-reqid=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++Mathematics&t=180&ask_summarization=1"},{"index":4,"title":"Kosinüs Fark Formülü Uygulaması","list":{"type":"unordered","items":["Kosinüs fark formülü: kosinüs(x-y) = kosinüs x × kosinüs y - sinüs x × sinüs y olarak veriliyor.","Tanjant ve kotanjant değerleri kullanılarak dik üçgenler çizilerek kosinüs ve sinüs değerleri hesaplanıyor.","Hesaplamalar sonucunda kosinüs x - y = 63/65 bulunuyor ve doğru cevap D şıkkı olarak belirleniyor."]},"beginTime":207,"endTime":319,"href":"/video/preview/11095231301459517085?parent-reqid=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++Mathematics&t=207&ask_summarization=1"},{"index":5,"title":"Tanjant Fark Formülü Uygulaması","list":{"type":"unordered","items":["İkinci soruda, alfa ile beta açıları arasındaki ilişki verilmiş ve kosinüs beta - kotanjant beta / alfa değerini bulmak isteniyor.","Tanjant fark formülü: tanjant(beta-alfa) = (tanjant beta - tanjant alfa) / (1 + tanjant beta × tanjant alfa) olarak veriliyor.","Dik üçgenler çizilerek tanjant değerleri hesaplanıyor ve sonuç 56/33 bulunuyor, doğru cevap B şıkkı olarak belirleniyor."]},"beginTime":319,"endTime":486,"href":"/video/preview/11095231301459517085?parent-reqid=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++Mathematics&t=319&ask_summarization=1"},{"index":6,"title":"Kosinüs Toplam ve Fark Formülleri","list":{"type":"unordered","items":["Üçüncü soruda, kosinüs x + y ve kosinüs x - y formülleri kullanılarak bir ifade sadeleştiriliyor.","Kosinüs toplam formülü: kosinüs(x+y) = kosinüs x × kosinüs y + sinüs x × sinüs y olarak veriliyor.","İşlemler sonucunda ifade -tan y olarak sadeleştiriliyor ve doğru cevap B şıkkı olarak belirleniyor."]},"beginTime":486,"endTime":602,"href":"/video/preview/11095231301459517085?parent-reqid=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++Mathematics&t=486&ask_summarization=1"},{"index":7,"title":"Trigonometrik İfadelerin Eşitliği","list":{"type":"unordered","items":["Dördüncü soruda, trigonometrik ifadenin hangi ifadeye eşit olduğu soruluyor.","Açıların eşit duruma getirilmesi için trigonometrik dönüşümler yapılıyor.","Kosinüs fark formülü kullanılarak ifade sadeleştiriliyor."]},"beginTime":602,"endTime":683,"href":"/video/preview/11095231301459517085?parent-reqid=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++Mathematics&t=602&ask_summarization=1"},{"index":8,"title":"Trigonometrik Formüllerin Kullanımı","list":{"type":"unordered","items":["Kosinüs formülünü kullanmak için açıları 90 dereceden çıkararak sinüs formülüne dönüştürmek mümkündür.","Sinüs formülünde isimler ters gelirken işaret aradaki açının aynısı olur.","Kosinüs formülünde isimler aynı gelirken işaret ters gelir."]},"beginTime":687,"endTime":1074,"href":"/video/preview/11095231301459517085?parent-reqid=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++Mathematics&t=687&ask_summarization=1"},{"index":9,"title":"Trigonometrik Denklemlerin Çözümü","list":{"type":"unordered","items":["Tanjant toplam formülü kullanılarak tanjant x değeri bulunabilir.","Kök 3 değeri tanjant 60 derece olarak yazılabilir.","Trigonometrik denklemlerde payda eşitleme yaparken, payda eşitlendikten sonra çarpım durumunda olan terimlerin de dikkate alınması gerekir."]},"beginTime":1074,"endTime":1290,"href":"/video/preview/11095231301459517085?parent-reqid=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++Mathematics&t=1074&ask_summarization=1"},{"index":10,"title":"Ters Trigonometrik Fonksiyonlar","list":{"type":"unordered","items":["Ters trigonometrik fonksiyonlarda arkların içerisindekileri bilmiyorsak, bunların bir açı olduğunu unutmamalıyız.","Sinüs toplam formülü kullanılarak sinüs alfa artı beta değeri bulunabilir.","Dik üçgenler çizerek bilinmeyen trigonometrik değerler hesaplanabilir."]},"beginTime":1290,"endTime":1428,"href":"/video/preview/11095231301459517085?parent-reqid=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++Mathematics&t=1290&ask_summarization=1"},{"index":11,"title":"Üçgenlerde Trigonometri","list":{"type":"unordered","items":["Üçgende açıların toplamı 180 dereceye eşittir.","Kosinüs toplam formülü kullanılarak üçgende açılar arasındaki ilişkiler bulunabilir.","Kosinüs 180 derece eksi bir açıya eşittir ve bu özellik üçgen problemlerinde kullanılabilir."]},"beginTime":1428,"endTime":1569,"href":"/video/preview/11095231301459517085?parent-reqid=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++Mathematics&t=1428&ask_summarization=1"},{"index":12,"title":"Üçgen Açıları ve Trigonometrik İşlemler","list":{"type":"unordered","items":["Üçgenin iç açılarının ölçüleri toplamı 180 derecedir ve tanjant C değeri sorulmaktadır.","C açısı, 180-A+B formülüyle hesaplanır ve tanjant C, tanjant (180-A+B) formülüyle -tanjant (A+B) olarak bulunur.","Tanjant (A+B) formülü kullanılarak tanjant C değeri -7/11 olarak hesaplanır."]},"beginTime":1574,"endTime":1696,"href":"/video/preview/11095231301459517085?parent-reqid=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++Mathematics&t=1574&ask_summarization=1"},{"index":13,"title":"Trigonometrik İfadelerin Çözümü","list":{"type":"unordered","items":["Tanjant x ve kotanjant y değerleri verilmiş, tanjant x+kotanjant y ifadesi istenmektedir.","Tanjant x ve kotanjant y ifadeleri sinüs ve kosinüs cinsinden yazıldıktan sonra payda eşitleme yapılır.","Kosinüs toplam formülü kullanılarak sinüs y çarpı kosinüs x değeri 3/5 olarak bulunur."]},"beginTime":1696,"endTime":1845,"href":"/video/preview/11095231301459517085?parent-reqid=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++Mathematics&t=1696&ask_summarization=1"},{"index":14,"title":"Sinüs Toplam Formülü Uygulaması","list":{"type":"unordered","items":["Sinüs x+60 sinüs x-60 ifadesi verilmiş ve tanjant x değeri istenmektedir.","Sinüs toplam formülü kullanılarak ifade düzenlenir ve sinüs x çarpı kosinüs 60° değeri 1/2 olarak bilinir.","İşlemler sonucunda tanjant x değeri -3√3 olarak bulunur."]},"beginTime":1845,"endTime":2011,"href":"/video/preview/11095231301459517085?parent-reqid=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++Mathematics&t=1845&ask_summarization=1"},{"index":15,"title":"Kosinüs Fark Formülü Uygulaması","list":{"type":"unordered","items":["Sinüs x-sinüs y ve kosinüs x-kosinüs y değerleri verilmiş, kosinüs x-y değeri istenmektedir.","Kosinüs fark formülü kullanılarak kosinüs x-y ifadesi hesaplanır.","İşlemler sonucunda kosinüs x-y değeri 7/12 olarak bulunur."]},"beginTime":2011,"endTime":2198,"href":"/video/preview/11095231301459517085?parent-reqid=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++Mathematics&t=2011&ask_summarization=1"},{"index":16,"title":"Trigonometrik İfadelerin Çözümü","list":{"type":"unordered","items":["Son soruda tanjant ifadelerinin değerleri hesaplanıyor.","İki kare farkı formülü kullanılarak tanjant kırk eksi tanjant on çarpı tanjant kırk artı tanjant on ifadesi çözülüyor.","Sonuç olarak tanjant otuz (kök üç bölü üç) çarpı tanjant elli (kök üç bölü üç) elde ediliyor ve cevap 142 olarak bulunuyor."]},"beginTime":2199,"endTime":2312,"href":"/video/preview/11095231301459517085?parent-reqid=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++Mathematics&t=2199&ask_summarization=1"},{"index":17,"title":"Gelecek Dersler Hakkında Bilgi","list":{"type":"unordered","items":["Sonraki derste şekilli sorular ele alınacak ve şekilli soruların gelme ihtimalinin yüksek olduğu belirtiliyor.","Yarım açı formülleri konusuna geçilecek ve sinüsün ayrıntılı çalışması yapılacak.","Yarım açı formüllerinin her yıl en az bir kez sorulduğu ve trigonometrik denklemlerde de kullanıldığı vurgulanıyor."]},"beginTime":2312,"endTime":2338,"href":"/video/preview/11095231301459517085?parent-reqid=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++Mathematics&t=2312&ask_summarization=1"}],"linkTemplate":"/video/preview/11095231301459517085?parent-reqid=1769730643839361-9461384520228357332-balancer-l7leveler-kubr-yp-vla-170-BAL&text=Vivek++Mathematics&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"80 Günde AYT Matematik Kampı | 34. 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