Question

已知sin（30°+a）=3/5,60°＜a＜150°，求cosa的值！！！ 求详细解析

Answer 1

sin(a+30)=3/5
cos(a+30)=-4/5
cosa=cos[(a+30)-30]
=cos(a+30)cos30+sin(a+30)sin30
=(-4/5)(√3/2)+(3/5)(1/2)
=(-4√3+3)/10

Answer 2

90<30+a<180
所以cos(30+a)<0
sin²(30+a)+cos²(30+a)=1
所以cos(30+a)=-4/5

所以cosa
=cos[(30+a)-30]
=cos(30+a)cos30+sin(30+a)sin30
=(-4√3/10+3)/10