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这是一堂关于“两角和与差的正余弦”习题课.学生的《课时作业》中有这样一道选择题:已知α∈(0,π/2),β∈(0,π/2),且sinα=5/13,cos(α+β)=-4/5,则sinβ的值为().A.33/65B.16/65C.56/65D.63/65应当说这是一道在角的变换背景下,考查两角和与差的正余弦公式的常规试题,而且两个角都是锐角,通过cos(α+β)=-4/5得到sin(α+β)=3/5,通过sinα=5/13得到cosα=12/13都是很容易理解的,因此由sinβ=sin(α+β-α)=sin(α+5β)cosα-cos(α+β)sinα就可以计算出sinβ的值为56/65,故选C.
This is an exercise on the “sine and cosine of the two corners and the difference.” There are multiple-choice questions in “Classwork Assignments” for students: α∈ (0, π / 2), β∈ / 2), and sinα = 5/13, cos (α + β) = - 4/5, the value of sinβ is (). A.33 / 65B.16 / 65C.56 / 65D.63 / 65 It should be said This is a conventional test of both positive and negative cosine formulas that examine both corners and in the context of corner transformations and both corners are acute and sin (α + β) is obtained by cos (α + β) = - 4/5 ) = 3/5, it is easy to understand that cosα = 12/13 by sinα = 5/13, so sinβ = sin α + β-α = sin α + β) sinα can calculate the value of sinβ 56/65, so choose C.