已知cos(π/6-θ)=a (|a|≦1)求cos(5π/6+θ)和sin(2π/3-θ)的值

问题描述:

已知cos(π/6-θ)=a (|a|≦1)求cos(5π/6+θ)和sin(2π/3-θ)的值

cos(5π/6+θ)=cos[π-(π/6-θ)]=-cos(π/6-θ)=-a sin(2π/3-θ)=sin[π/2+(π/6-θ)]=cos(π/6+θ)=a

思路:重点是变角,可把第一问中 5派/6 写成 派-派/6,第二问中 2派/3 写成 派/2+派/6,再分别用诱导公式解决,最终得一问为-a,二问为a