Question

已知锐角α的正弦值为3/5.(1)求cosα和cos(π/2+α)的值;(2)判断点P(cos2α,sin2α)所在象限

Answer 1

1.

α为锐角,则

cosα=√（1-sin^2 α)=4/5;

cos(π/2+α)=-cos[π-(π/2+α)]=-cos(π/2-α)=-sinα=-3/5;

2.

cos2α=1-2sin^2 α=7/25＞0,

sin2α=2·sinα·cosα一定＞0(α是锐角,故正余弦都大于0),

所以P(cos2α,sin2α)在第一象限