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
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![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](/uploads/image/z/12266235-27-5.jpg?t=%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fa%3D%28sin%CE%B8%2C2%29%2Cb%3D%28cos%CE%B8%2C1%29%2Ca%2F%2Fb%2C%CE%B8%E5%B1%9E%E4%BA%8E%280%2Cpi%2F2%29%281%29%E6%B1%82sin%CE%B8%2C%E5%92%8Ccos%CE%B8%E7%9A%84%E5%80%BC%282%29%E8%8B%A5sin%28%CE%B8-w%29%3D3%2F5%2C0)
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