Question

a是锐角sin(a-30°)=1/3,求cosa

Answer 1

a-30°可能是锐角,也可能是负角,但是一、四象限角,余弦值为正,

cos(a-30°)=√[1-sin^2(a-30°)]=√2/3,

cosa=cos(a-30°+30°)=cos(a-30°)cos30°-sin(a-30°)*sin30°

=(√2/3)*√3/2-(1/3)*(1/2)

=(√6-1)/6.