已知sinx=7分之4倍根号3,sin(x-y)=14分之3倍根号3,且1＜y＜x＜2分之π,求y的值

题目

已知sinx=7分之4倍根号3,sin(x-y)=14分之3倍根号3,且1＜y＜x＜2分之π,求y的值

答案

cosx=1/7
cos(x-y)=13/14
siny
=sin(x-(x-y))
=sinxcos(x-y)-cosxsin(x-y)
=4√3/7*13/14-1/7*3√3/14
=√3/2
所以y=π/3