Trigonometri-17 | Trigonometrik Denklemler-2 | AYT Matematik
Yayın tarihi 2 haz 20202 haz 2020
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Denklemler","list":{"type":"unordered","items":["Tanjant x × tanjant 5x = 1 denkleminin π/2 aralığındaki çözüm kümesi x = π/18 + π/9k şeklindedir.","Tanjant 4x × tanjant 5x = 1 denkleminin çözüm kümesi, tanjant x × kotanjant x = 1 özdeşliğinden de bulunabilir.","Sinüs 3x = kosinüs 3x denkleminin çözüm kümesi x = 12° + 36°k şeklindedir."]},"beginTime":479,"endTime":751,"href":"/video/preview/15713436361816481627?channelId=d3d3LnlvdXR1YmUuY29tO1VDRTNzbzI3aFFxUDBzbmtYc0p6MXFXZw%3D%3D&how=tm&parent-reqid=1752661558506297-15855290930615572526-balancer-l7leveler-kubr-yp-klg-33-BAL&text=MET%C4%B0N+HOCAM&t=479&ask_summarization=1"},{"index":4,"title":"Trigonometrik Denklemlerin Farklı Çözüm Yöntemleri","list":{"type":"unordered","items":["Kosinüs x + sinüs x = 0 denkleminde, sinüs x/kosinüs x = tanjant x şeklinde sadeleştirme yapılabilir.","Tanjant x = -√3 denkleminin çözüm kümesi x = -60° + 180°k 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bulunur."]},"beginTime":817,"endTime":949,"href":"/video/preview/15713436361816481627?channelId=d3d3LnlvdXR1YmUuY29tO1VDRTNzbzI3aFFxUDBzbmtYc0p6MXFXZw%3D%3D&how=tm&parent-reqid=1752661558506297-15855290930615572526-balancer-l7leveler-kubr-yp-klg-33-BAL&text=MET%C4%B0N+HOCAM&t=817&ask_summarization=1"},{"index":6,"title":"Kotanjant Denklemleri","list":{"type":"unordered","items":["Kosinüs x eşittir eksi sinüs x denklemi çözülerek kotanjant x eşittir üç bulunur, ancak müfredat dahilinde hangi açının kotanjantı üç olduğunu bilmek zorunlu değildir.","Kotanjant x eşittir eksi bir denklemi çözülerek x eşittir 3π/4 bulunur.","Trigonometrik denklemlerde kökler bulunurken, aralık dışına çıkmamak için turlama sistemi kullanılır."]},"beginTime":949,"endTime":1052,"href":"/video/preview/15713436361816481627?channelId=d3d3LnlvdXR1YmUuY29tO1VDRTNzbzI3aFFxUDBzbmtYc0p6MXFXZw%3D%3D&how=tm&parent-reqid=1752661558506297-15855290930615572526-balancer-l7leveler-kubr-yp-klg-33-BAL&text=MET%C4%B0N+HOCAM&t=949&ask_summarization=1"},{"index":7,"title":"Tanjant Denklemleri","list":{"type":"unordered","items":["Tanjant denklemlerinde önce payda eşitleme yapılır ve tanjant 2x formülü kullanılarak denklem çözülür.","Tanjant x eşittir 30 derece denklemi çözülerek x eşittir 30 derece bulunur.","Tanjant x eksi iki kotanjant x eşittir bir denkleminin çözüm kümesi, tanjant x eşittir iki ve tanjant x eşittir eksi bir denklemlerinin çözümleriyle 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Sınıf matematik trigonometrik denklemler konu anlatımı ve soru çözümü. Patreon Üzerinden Destek Olmak İçin...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/4526735/bc8157e99927bbaa13210b0d2b71f683/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/CKvPagEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"0","reqid":"1752661558506297-15855290930615572526-balancer-l7leveler-kubr-yp-klg-33-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1752661558506297-15855290930615572526-balancer-l7leveler-kubr-yp-klg-33-BAL&text=videoid:15713436361816481627","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik öğretmeninin trigonometrik denklemler konusunu anlattığı eğitim içeriğidir.","Videoda tanjant, kotanjant, sinüs ve kosinüs denklemlerinin çözüm yöntemleri detaylı şekilde ele alınmaktadır. Öğretmen önce teorik bilgileri açıklamakta, ardından çeşitli örnek sorular üzerinden çözüm tekniklerini göstermektedir. Özellikle tanjant ve kotanjantın periyotlarının π olduğu, yarım açı açılımları ve ikinci dereceden denklemlerin çözümü gibi konular üzerinde durulmaktadır.","Video, bir sonraki derste daha karmaşık soruların çözüleceği bilgisiyle sonlanmaktadır."]},"endTime":1409,"title":"Trigonometrik Denklemler Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Tanjant ve Kotanjant Denklemleri","list":{"type":"unordered","items":["Bu derste tanjant ve kotanjant denklemleri çözülecek, bu denklemler nispeten daha rahat çözülebilir çünkü sadece bir çözüm kümesi bulunur.","Tanjant ve kotanjantın periyodu π olduğundan, tanjant x = a veya kotanjant x = a denklemlerini çözerken sadece bir çözüm yeterlidir.","Tanjant ve kotanjant fonksiyonlarının tanımlarına göre, ikinci bölgede negatif, üçüncü bölgede pozitif değer alırlar."]},"beginTime":0,"endTime":86,"href":"/video/preview/15713436361816481627?channelId=d3d3LnlvdXR1YmUuY29tO1VDRTNzbzI3aFFxUDBzbmtYc0p6MXFXZw%3D%3D&how=tm&parent-reqid=1752661558506297-15855290930615572526-balancer-l7leveler-kubr-yp-klg-33-BAL&text=MET%C4%B0N+HOCAM&t=0&ask_summarization=1"},{"index":1,"title":"Tanjant ve Kotanjant Denklemlerinin Çözümü","list":{"type":"unordered","items":["Tanjant x = tanjant alfa veya kotanjant x = kotanjant alfa denklemlerinde, işaretler aynıysa (artı-artı veya eksi-eksi) x = alfa + πk şeklinde çözüm bulunur.","İşaretler farklıysa (artı-eksi veya eksi-artı), tanjant ve kotanjant tek fonksiyonlar olduğu için eksi işareti içeri atılarak x = -alfa + πk şeklinde çözüm bulunabilir.","Tanjant x = √3 denkleminin -360 aralığındaki en büyük kökü 230 derecedir."]},"beginTime":86,"endTime":293,"href":"/video/preview/15713436361816481627?channelId=d3d3LnlvdXR1YmUuY29tO1VDRTNzbzI3aFFxUDBzbmtYc0p6MXFXZw%3D%3D&how=tm&parent-reqid=1752661558506297-15855290930615572526-balancer-l7leveler-kubr-yp-klg-33-BAL&text=MET%C4%B0N+HOCAM&t=86&ask_summarization=1"},{"index":2,"title":"Trigonometrik Denklemlerin Çözümü Örnekleri","list":{"type":"unordered","items":["Tanjant 2x = 0 denkleminin çözüm kümesi x = π/2k şeklindedir.","Kotanjant 6x = -√3/3 denkleminin çözüm kümesi x = -π/6 + π/6k veya x = -30° + 30°k şeklindedir.","Tanjant 4x = kotanjant 2x denkleminin çözüm kümesi x = 10° + 50°k şeklindedir."]},"beginTime":293,"endTime":479,"href":"/video/preview/15713436361816481627?channelId=d3d3LnlvdXR1YmUuY29tO1VDRTNzbzI3aFFxUDBzbmtYc0p6MXFXZw%3D%3D&how=tm&parent-reqid=1752661558506297-15855290930615572526-balancer-l7leveler-kubr-yp-klg-33-BAL&text=MET%C4%B0N+HOCAM&t=293&ask_summarization=1"},{"index":3,"title":"Karmaşık Trigonometrik Denklemler","list":{"type":"unordered","items":["Tanjant x × tanjant 5x = 1 denkleminin π/2 aralığındaki çözüm kümesi x = π/18 + π/9k şeklindedir.","Tanjant 4x × tanjant 5x = 1 denkleminin çözüm kümesi, tanjant x × kotanjant x = 1 özdeşliğinden de bulunabilir.","Sinüs 3x = kosinüs 3x denkleminin çözüm kümesi x = 12° + 36°k şeklindedir."]},"beginTime":479,"endTime":751,"href":"/video/preview/15713436361816481627?channelId=d3d3LnlvdXR1YmUuY29tO1VDRTNzbzI3aFFxUDBzbmtYc0p6MXFXZw%3D%3D&how=tm&parent-reqid=1752661558506297-15855290930615572526-balancer-l7leveler-kubr-yp-klg-33-BAL&text=MET%C4%B0N+HOCAM&t=479&ask_summarization=1"},{"index":4,"title":"Trigonometrik Denklemlerin Farklı Çözüm Yöntemleri","list":{"type":"unordered","items":["Kosinüs x + sinüs x = 0 denkleminde, sinüs x/kosinüs x = tanjant x şeklinde sadeleştirme yapılabilir.","Tanjant x = -√3 denkleminin çözüm kümesi x = -60° + 180°k 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bulunur."]},"beginTime":817,"endTime":949,"href":"/video/preview/15713436361816481627?channelId=d3d3LnlvdXR1YmUuY29tO1VDRTNzbzI3aFFxUDBzbmtYc0p6MXFXZw%3D%3D&how=tm&parent-reqid=1752661558506297-15855290930615572526-balancer-l7leveler-kubr-yp-klg-33-BAL&text=MET%C4%B0N+HOCAM&t=817&ask_summarization=1"},{"index":6,"title":"Kotanjant Denklemleri","list":{"type":"unordered","items":["Kosinüs x eşittir eksi sinüs x denklemi çözülerek kotanjant x eşittir üç bulunur, ancak müfredat dahilinde hangi açının kotanjantı üç olduğunu bilmek zorunlu değildir.","Kotanjant x eşittir eksi bir denklemi çözülerek x eşittir 3π/4 bulunur.","Trigonometrik denklemlerde kökler bulunurken, aralık dışına çıkmamak için turlama sistemi 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