已知角θ的顶点与原点重合,始边与x轴的正半轴重合,终边在直线y=2x上,则cos2θ=求详细答案,

Question

已知角θ的顶点与原点重合,始边与x轴的正半轴重合,终边在直线y=2x上,则cos2θ=求详细答案,

Answer 1

终边在直线y=2x上
设θ终边一点P(x,y),y=2x,x≠0
则tanθ=y/x=2x/x=2
∴cos2θ=cos²θ-sin²θ
=(cos²θ-sin²θ)/(cos²θ+sin²θ) (∵ cos²θ+sin²θ=1)
=(1-sin²θ/cos²θ)/(1+sin²θ/cos²θ) (分子分母同时除以cos²θ)
=(1-tan²θ)/(1+tan²θ)
=(1-4)/(1+4)
=-3/5