Question

已知sin(30°+α)=3/5,60°<α<150°,求cosα的值

Answer 1

90<30°+α<180 30°+α是第二象限
sin(30°+α)=3/5,,则cos（30°+α)=-4/5
cosa=cos((30°+α)-30)=cos((30°+α)sin30+sin((30°+α)cos30
=-4/5X1/2+3/5X根号3/2
=-4/10+3根号3/10
=(-4+根号3）/10
因为a的值横跨第一第二象限，尽量保持a的完整性。

Answer 2

希望你能采纳我的意见，谢谢~sin(30°+α）=3/5,
60°＜α＜150°
所以30°+60°<a+30°<30°+150°
90°<a+30°<180°
所以 a+30° 是第二象限角
cos(a+30°)<0
得 cos（30°+α）=-4/5

Answer 3

已知sin(30°+α)=3/5,60°<α<150°,
cos(30°+α)=-4/5,
cosa=cos[(30°+α)-30°]
=cos(30°+α)cos30°+sin(30°+α)sin30°
=-4/5*√3/2+3/5*1/2
=(3-4√3)/10