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ise bağımlı değişkendir.","Bağımsız değişken (x) değiştirildiğinde, bağımlı değişken (y) otomatik olarak değişir."]},"beginTime":205,"endTime":318,"href":"/video/preview/2789839763497731552?parent-reqid=1769797666650378-12155992629491439154-balancer-l7leveler-kubr-yp-vla-193-BAL&text=Mat+Ematica&t=205&ask_summarization=1"},{"index":4,"title":"Doğrusal İlişkinin Tanımı","list":{"type":"unordered","items":["İki değişken arasında eşit aralıklarda sabit bir değişim oranı varsa bu ilişkiye doğrusal denir.","Örnek olarak Şakir'in çalıştığı fabrikada üretilen sabunların özdeş kolilere doldurulması problemi verilmiştir."]},"beginTime":318,"endTime":346,"href":"/video/preview/2789839763497731552?parent-reqid=1769797666650378-12155992629491439154-balancer-l7leveler-kubr-yp-vla-193-BAL&text=Mat+Ematica&t=318&ask_summarization=1"},{"index":5,"title":"Doğrusal Fonksiyonlar","list":{"type":"unordered","items":["Zaman değiştikçe koli sayısı artıyor; birinci dakikada 7 koli, ikinci dakikada 14 koli, 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Matematik 10.Sınıf Matematik Yeni Müfredat Maarif Model tüm konularını konu sıralamasına uygun şekilde tanımlarla kavramlarla ispatlarla birlikte öğreneceğiz. 1.Tema Geometrik Şekiller...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3383616/3d084fc38e5b6c2a56e52cb76d8c8f79/564x318_1"},"target":"_self","position":"2","reqid":"1769797666650378-12155992629491439154-balancer-l7leveler-kubr-yp-vla-193-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769797666650378-12155992629491439154-balancer-l7leveler-kubr-yp-vla-193-BAL&text=videoid:13163913345582469369","teaser":[{"list":{"type":"unordered","items":["Bu video, Mehmet Hoca tarafından Rehber Matematik kanalında sunulan 10. sınıf matematik dersidir. Öğretmen, yeni Maarif modeline uygun şekilde trigonometri konusunu anlatmaktadır.","Video, dik üçgende trigonometrik oranlar (sinüs, kosinüs, tanjant, kotanjant) konusunu kapsamlı şekilde ele almaktadır. İlk olarak temel trigonometrik oranlar tanımlanmakta, ardından özel dik üçgenler (3-4-5, 7-24-25, 8-15-17) kullanılarak örnekler çözülmektedir. Daha sonra benzer üçgenlerde trigonometrik oranların eşitliği ve sin²α + cos²α = 1, tanα × cotα = 1 gibi trigonometrik özdeşlikler ispatlanmaktadır.","Videoda ayrıca not alma teknikleri, soru avcısı bölümü ve pratik problemler çözülmektedir. Öğretmen, trigonometrik değerlerin ezberlenmeden mantığının öğrenilmesi gerektiğini vurgulamakta ve Pisagor bağıntısı kullanarak ispatlar yapmaktadır. Video, 10 sorudan oluşan bir dersin son bölümünü oluşturmaktadır."]},"endTime":3407,"title":"10. Sınıf Matematik: Dik Üçgende Trigonometrik Oranlar ve Özdeşlikler","beginTime":0}],"fullResult":[{"index":0,"title":"10. Sınıf Matematik Derslerine Giriş","list":{"type":"unordered","items":["Mehmet hocanın Rehber Matematik kanalında 10. sınıf yeni Maarif modele uygun matematik dersleri başlıyor.","Tüm PDF'ler ve soru avcıları ücretsiz olarak Instagram hesabından paylaşılacak.","10. sınıf matematik müfredatı tanımıyla, kavramıyla ve ispatıyla birlikte bitirilecek."]},"beginTime":0,"endTime":98,"href":"/video/preview/13163913345582469369?parent-reqid=1769797666650378-12155992629491439154-balancer-l7leveler-kubr-yp-vla-193-BAL&text=Mat+Ematica&t=0&ask_summarization=1"},{"index":1,"title":"Yeni Maarif Modeli ve Sınav Sistemi","list":{"type":"unordered","items":["Derslerin tek amacı okul notları değil, yeni Maarif model ve sınav sistemine hazırlıklı olmak.","12. sınıfa geldiğinde sınav sistemi değişeceği için bu konuları canavar gibi öğrenmek gerekiyor.","Bu seneki 10. sınıf matbu kitabı yetiştirilemedi, önümüzdeki sene 11. sınıf matbook'u PDF'lerle değil kitaplarla oluşturulacak."]},"beginTime":98,"endTime":133,"href":"/video/preview/13163913345582469369?parent-reqid=1769797666650378-12155992629491439154-balancer-l7leveler-kubr-yp-vla-193-BAL&text=Mat+Ematica&t=98&ask_summarization=1"},{"index":2,"title":"Dik Üçgende Trigonometrik Oranlar","list":{"type":"unordered","items":["Birinci tema \"Geometrik Şekiller\" ve kazanım \"Dik Üçgende Trigonometrik Oranlar\" (sinüs, kosinüs, tanjant, kotanjant ve trigonometrik özdeşlikler).","Trigonometri, Latincede \"üç\" anlamına gelen \"tri\" ve \"açı\" anlamına gelen \"gonometri\" kelimelerinden oluşur ve üçgenlerle alakalı bir mevzudur.","Dik üçgende, 90 derecenin karşısındaki kenara hipotenüs, alfa açısının karşısındaki kenara karşı dik kenar, komşu dik kenara komşu dik kenar 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Üçgenler","list":{"type":"unordered","items":["Dik üçgenlerde trigonometrik oranlar (sinüs, kosinüs, tanjant, kotanjant) hesaplanırken karşı dik kenar, komşu dik kenar ve hipotenüs kullanılır.","Özel dik üçgenler (3-4-5, 7-24-25, 8-15-17) kenar oranları ile ilgili işlemler yapılabilir ve Pisagor bağıntısına girmeden doğrudan hesaplanabilir.","Sinüs alfa = karşı dik kenar / hipotenüs, kosinüs alfa = komşu dik kenar / hipotenüs, tanjant alfa = karşı dik kenar / komşu dik kenar, kotanjant alfa = komşu dik kenar / karşı dik kenar formülleri kullanılır."]},"beginTime":395,"endTime":704,"href":"/video/preview/13163913345582469369?parent-reqid=1769797666650378-12155992629491439154-balancer-l7leveler-kubr-yp-vla-193-BAL&text=Mat+Ematica&t=395&ask_summarization=1"},{"index":5,"title":"Trigonometrik Özdeşlikler","list":{"type":"unordered","items":["Alfa ile beta açılarının toplamı 90 derece ise, sinüs alfa = kosinüs beta olur.","Tanjant alfa ile kotanjant beta değerleri birbirine eşittir.","Sinüs alfa² + kosinüs alfa² = 1 özdeşliği vardır."]},"beginTime":704,"endTime":896,"href":"/video/preview/13163913345582469369?parent-reqid=1769797666650378-12155992629491439154-balancer-l7leveler-kubr-yp-vla-193-BAL&text=Mat+Ematica&t=704&ask_summarization=1"},{"index":6,"title":"Trigonometrik Değerler ve Dik Üçgenler","list":{"type":"unordered","items":["Trigonometrik değerler (tanjant, kotanjant, kosinüs, sinüs) dik üçgenlerde hesaplanır.","Tanjant, karşı dik kenar bölü komşu dik kenardır; kotanjant ise komşu dik kenar bölü karşı dik kenardır.","Trigonometrik değerleri hesaplamak için dik üçgen çizmek gerekir ve açıların ölçüsü 90 derece olmalıdır."]},"beginTime":901,"endTime":1106,"href":"/video/preview/13163913345582469369?parent-reqid=1769797666650378-12155992629491439154-balancer-l7leveler-kubr-yp-vla-193-BAL&text=Mat+Ematica&t=901&ask_summarization=1"},{"index":7,"title":"Trigonometrik Değerlerin Hesaplanması","list":{"type":"unordered","items":["39 birim uzunluğundaki çubuğun duvara uzaklığı 15 birimdir ve zemine değdiği nokta sabit kalacak biçimde duvara doğru devrildiğinde zeminle alfa derecelik bir dar açı oluşturur.","Sinüs alfa, kosinüs alfa ve kotanjant alfa değerleri hesaplanırken, kenar uzunlukları Pisagor teoremi veya özel dik üçgenler kullanılarak bulunur.","Benzer üçgenlerde eşit açıların karşısındaki kenarların oranları birbirine eşittir."]},"beginTime":1106,"endTime":1412,"href":"/video/preview/13163913345582469369?parent-reqid=1769797666650378-12155992629491439154-balancer-l7leveler-kubr-yp-vla-193-BAL&text=Mat+Ematica&t=1106&ask_summarization=1"},{"index":8,"title":"Benzer Üçgenlerde Trigonometrik Değerler","list":{"type":"unordered","items":["İki benzer dik üçgende, birbirini 90 dereceye tamamlayan açıların trigonometrik değerleri (sinüs-kosinüs, tanjant-kotanjant) birbirine eşittir.","Benzer üçgenlerde kenar uzunlukları orantılıdır ve bu oran trigonometrik değerleri hesaplamada kullanılır.","Kenar-açı-kenar benzerliği veya kenar-kenar-kenar bağıntısı kullanılarak benzer üçgenler belirlenebilir."]},"beginTime":1412,"endTime":1586,"href":"/video/preview/13163913345582469369?parent-reqid=1769797666650378-12155992629491439154-balancer-l7leveler-kubr-yp-vla-193-BAL&text=Mat+Ematica&t=1412&ask_summarization=1"},{"index":9,"title":"Benzer Üçgenlerde Trigonometrik Değerler","list":{"type":"unordered","items":["Benzer üçgenlerde eşit açıların trigonometrik değerleri birbirine eşittir.","Benzer üçgenlerin eşit açılarına ait trigonometrik oranlar eşittir.","Bir üçgende sinüs A açısı ile başka bir üçgende sinüs B açısı eşitse, bu açılar birbirine eşittir."]},"beginTime":1590,"endTime":1724,"href":"/video/preview/13163913345582469369?parent-reqid=1769797666650378-12155992629491439154-balancer-l7leveler-kubr-yp-vla-193-BAL&text=Mat+Ematica&t=1590&ask_summarization=1"},{"index":10,"title":"Trigonometrik Oranların Özellikleri","list":{"type":"unordered","items":["Dar açının trigonometrik oranları verilirse, diğer trigonometrik oranlara ulaşmak için dik üçgen çizilir.","Bir açının trigonometrik oranı biliniyorsa, kenar uzunlukları aynı olmak zorunda değildir, katları olabilir.","Benzer üçgenlerde aynı açıların trigonometrik değerleri eşittir, ancak kenar uzunlukları farklı olabilir."]},"beginTime":1724,"endTime":1840,"href":"/video/preview/13163913345582469369?parent-reqid=1769797666650378-12155992629491439154-balancer-l7leveler-kubr-yp-vla-193-BAL&text=Mat+Ematica&t=1724&ask_summarization=1"},{"index":11,"title":"Özel Üçgenler ve Trigonometrik Değerler","list":{"type":"unordered","items":["5-12-13 üçgeninde sinüs alfa değeri 12/13, kosinüs alfa değeri 5/13, tanjant alfa değeri 12/5 ve kotanjant alfa değeri 5/12'dir.","8-15-17 özel üçgeninde sinüs beta değeri 8/17, kosinüs beta değeri 15/17, tanjant beta değeri 8/15'tir.","Trigonometrik oranlar hesaplanırken karşı kenar bölü komşu kenar veya komşu kenar bölü karşı kenar formülü kullanılır."]},"beginTime":1840,"endTime":2041,"href":"/video/preview/13163913345582469369?parent-reqid=1769797666650378-12155992629491439154-balancer-l7leveler-kubr-yp-vla-193-BAL&text=Mat+Ematica&t=1840&ask_summarization=1"},{"index":12,"title":"Trigonometrik Değerler ve Dik Üçgenler","list":{"type":"unordered","items":["Trigonometrik değerler hesaplamak için dik üçgen çizmek gerekir.","Sinüs alfa, karşı kenar bölü hipotenüs; kosinüs alfa, komşu kenar bölü hipotenüs; tanjant alfa, karşı kenar bölü komşu kenar; kotanjant alfa, komşu kenar bölü karşı kenar formülleri kullanılır.","Paydada köklü ifade kalırsa, genişletme işlemi yaparak köklü ifadeyi paydan kaldırabiliriz."]},"beginTime":2044,"endTime":2175,"href":"/video/preview/13163913345582469369?parent-reqid=1769797666650378-12155992629491439154-balancer-l7leveler-kubr-yp-vla-193-BAL&text=Mat+Ematica&t=2044&ask_summarization=1"},{"index":13,"title":"Gölge Problemi","list":{"type":"unordered","items":["Bir parkta 9 metre 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Playlist for Olympiad and admissions questions from other countries and universities: My Olympiad Math Records: http://bit.ly/tunckurtolimpiyat...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2177248/a0c4ce7404e4beef9f094e0dccc2c35d/564x318_1"},"target":"_self","position":"5","reqid":"1769797666650378-12155992629491439154-balancer-l7leveler-kubr-yp-vla-193-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769797666650378-12155992629491439154-balancer-l7leveler-kubr-yp-vla-193-BAL&text=videoid:9613666390587702260","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik eğitmeni tarafından sunulan matematik dersidir. Eğitmen, Azerbaycan'dan bir takipçinin gönderdiği ve Rusya matematik olimpiyatında sorulmuş olduğu iddia edilen bir problemi çözmektedir.","Video iki ana bölümden oluşmaktadır. İlk bölümde 750x + 7x² + 7x³ = 14 eşitliğini çözmek için polinom teoremi ve cebirsel yaklaşım kullanılarak iki farklı yöntem gösterilmektedir. İkinci bölümde ise karmaşık sayıların temel kavramları (gösterimi, karmaşık düzlemde gösterimi, normu ve argümanı) ve logaritma ile ilişkisi anlatılmaktadır.","Videoda ayrıca karmaşık sayıların logaritma içinde nasıl yazılacağı gösterilmekte ve bir denklem sisteminin çözümü ile karmaşık sayıların logaritma ile ilişkisi açıklanmaktadır. Video sonunda, Berkeday'in matematik yarışmasının 2012 sorusu da çözüleceği belirtilmektedir."]},"endTime":922,"title":"Matematik Dersi: Polinomlar ve Karmaşık Sayılar","beginTime":0}],"fullResult":[{"index":0,"title":"Giriş ve Soru Tanıtımı","list":{"type":"unordered","items":["Sunucu, Azerbaycan'dan gelen bir takipçinin sorusu üzerine bir matematik problemi çözeceğini belirtiyor.","Kanalda Polonya ve İspanya'daki üniversitelerin kabul sorularını da çözdüklerini paylaşıyor.","Bu sorunun Rusya'da yapılan bir matematik olimpiyatında sorulduğu söyleniyor, ancak bu bilginin doğruluğu sorgulanıyor."]},"beginTime":8,"endTime":70,"href":"/video/preview/9613666390587702260?parent-reqid=1769797666650378-12155992629491439154-balancer-l7leveler-kubr-yp-vla-193-BAL&text=Mat+Ematica&t=8&ask_summarization=1"},{"index":1,"title":"W Fonksiyonu Hakkında Bilgi","list":{"type":"unordered","items":["Sunucu, W fonksiyonu ile ilgili bir video yapacağını ve bu fonksiyonun x üzeri x eşittir iki gibi soruları çözerken kullanıldığını belirtiyor.","W fonksiyonunun genel kültür olarak anlatılacağını, lisansta analiz veya advanced calculus derslerinde de karşılaşılacağını söylüyor."]},"beginTime":70,"endTime":102,"href":"/video/preview/9613666390587702260?parent-reqid=1769797666650378-12155992629491439154-balancer-l7leveler-kubr-yp-vla-193-BAL&text=Mat+Ematica&t=70&ask_summarization=1"},{"index":2,"title":"Matematik Probleminin Çözümü","list":{"type":"unordered","items":["750x + 7x² + 7x³ = 14 denklemi verilmiş ve 14'ün bu denklemde özel bir değeri olduğu belirtiliyor.","u dönüşümü uygulanarak denklem u³ + u² + u = 14 şeklinde yeniden düzenleniyor.","Fermat teoremi kullanılarak, polinomun sabiti (14) köklerine tam bölünmesi gerektiği ve bu nedenle x-2'nin kök olduğu tespit 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sanal veya imajiner kısmı bir noktada, reel kısmı ise orijinden uzaklık olarak temsil edilir.","Karmaşık sayının normu (boyu) reel kısmının karesi ile sanal kısmının karesinin toplamının kareköküdür."]},"beginTime":417,"endTime":640,"href":"/video/preview/9613666390587702260?parent-reqid=1769797666650378-12155992629491439154-balancer-l7leveler-kubr-yp-vla-193-BAL&text=Mat+Ematica&t=417&ask_summarization=1"},{"index":5,"title":"Karmaşık Sayıların Gösterimi","list":{"type":"unordered","items":["Karmaşık sayılar e üzeri i theta şeklinde gösterilebilir, burada e üzeri i theta = cos(theta) + i sin(theta) olarak hesaplanır.","Karmaşık sayılar periyodiktir, yani e üzeri i(theta+2kπ) şeklinde yazılabilir, burada k tam sayıdır.","Logaritmanın içinde i ifadeleri yazılabilir ve bu durumda kompleks logaritma olarak 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