已知向量a=(sinθ,2),b=(cosθ,1),a//b,θ属于(0,pi/2)(1)求sinθ,和cosθ的值(2)若sin(θ-w)=3/5,0

已知向量a=(sinθ,2),b=(cosθ,1),a//b,θ属于(0,pi/2)(1)求sinθ,和cosθ的值(2)若sin(θ-w)=3/5,0
已知向量a=(sinθ,2),b=(cosθ,1),a//b,θ属于(0,pi/2)
(1)求sinθ,和cosθ的值
(2)若sin(θ-w)=3/5,0

已知向量a=(sinθ,2),b=(cosθ,1),a//b,θ属于(0,pi/2)(1)求sinθ,和cosθ的值(2)若sin(θ-w)=3/5,0
已知向量a=(sinθ,2),b=(cosθ,1),a//b,θ属于(0,pi/2)
(1)求sinθ,和cosθ的值
sinθ/cosθ=2/1=2
tanθ=2 tan²θ=4
1+tan²θ=sec²θ=5 cos²θ=1/5 sin²θ=4/5
θ属于(0,pi/2)
cosθ=1/√5 sinθ=2/√5
(2)sin(θ-w)=3/5
=sinθcosw-cosθsinw
=2/√5cosw-1/√5sinw=3/5
4/√5cosw-2/√5sinw=6/5 (1)
cos(θ-w)=4/5
= cosθcosw+sinθsinw
=1/√5cosw+2/√5sinw=4/5 (2)
(1)+(2) √5cosw=2
cosw=2/√5