角a是锐角,cos(a-π/4)=4/5那么sina=多少

问题描述:

角a是锐角,cos(a-π/4)=4/5那么sina=多少
cos(a - π/4)cosπ/4 + sin(a - π/4)sinπ/4 =
= 4/5 x √2/2 + 3/5 x √2/2
这步为什么?

sina =cos(π/2 - a) = cos(a - π/2) = cos( a - π/4 - π/4)
= cos(a - π/4)cosπ/4 + sin(a - π/4)sinπ/4 =
= 4/5 x √2/2 + 3/5 x √2/2 = 7/5 x √2/2 = 7√2/10