已知sin^2α/sin^2β+cos^2αcos^2θ=1 若α＝9π／4,β＝13π／3 求|sinθ|的值

题目

已知sin^2α/sin^2β+cos^2αcos^2θ=1 若α＝9π／4,β＝13π／3 求|sinθ|的值

答案

α＝9π/4=2π+π/4
sinα=sin(π/4)=√2/2,cosα=cos(π/4)=√2/2
sin²α=cos²α=1/2
β＝13π/3=4π+π/3
sinβ=sin(π/3)=√3/2
sin²β=3/4
sin²α/sin²β+cos²αcos²θ=1
(1/2)/(3/4)+1/2*cos²θ=1
cos²θ=2/3
|sinθ|=√(1-cos²θ)=√(1-2/3)=√(1/3)=√3/3