
已知a∈(0,π/2),b∈(-π,-π/2),若sin(a-b)=3/5,cosa=3/4,求sinb 要过程
1个回答
展开全部
a∈(0,π/2)
b∈(-π,-π/2)
则
a-b∈(π/2,3π/2)
sin(a-b)=3/5
则
cos(a-b)=-4/5
cosa=3/4
则
sina=√7/4
sinb
=-sin(a-b-a)
=-sin(a-b)cos(a)+cos(a-b)sina
=-(3/5)*(3/4)+(-4/5)*(√7/4)
=- (9+4√7)/20
b∈(-π,-π/2)
则
a-b∈(π/2,3π/2)
sin(a-b)=3/5
则
cos(a-b)=-4/5
cosa=3/4
则
sina=√7/4
sinb
=-sin(a-b-a)
=-sin(a-b)cos(a)+cos(a-b)sina
=-(3/5)*(3/4)+(-4/5)*(√7/4)
=- (9+4√7)/20
推荐律师服务:
若未解决您的问题,请您详细描述您的问题,通过百度律临进行免费专业咨询