Question

已 知:sin(30°＋α)＝3/5，60°＜α＜150°，求cosα 的值。

Answer 1

因为60°＜α＜150°
所以90°＜30°+α＜180°
在这个区间的余弦值为负值。
即cos(30°+α)<0
因为sin(30°+α)^2
+
cos(30°+α)^2
=
1
所以cos(30°+α)^2
=
1
-
(3/5)^2
=
1
-
9/25
=
16/弗单缔竿郫放惦虱定僵25
即cos(30°+α)
=
-4/5
希望有用。

Answer 2

∵60°＜α＜150°
∴90°<30°+α<180°
则cos(30°+α)<0
∴cos(30°+α)=-√[1-sin²(30°+α)]=-√[1-(3/5)²]=-4/5
而sin30°=1/2
cos30°=√3/2
那么cosα
=cos[(30°+α)-30°]
=cos(30°+α)cos30°+sin(30°+α)sin30°
=-4/5×√3/2+3/5×1/2
=(3-4√3)/10