已知函数f(x)=2sin(1/3x-π/6),x∈R,

题目

已知函数f(x)=2sin(1/3x-π/6),x∈R,
求f(5π/4)的值
设a,b∈[0,π/2],f(3a+π/2)=10/13,f(3b+2π=6/5,求cos(a+b）的值

答案

f(3α+π/2)=2sin(α+π/6-π/6)=2sinα=10/13 sinα=5/13
f(3β+2π）=2sin（β+π/2）=6/5 cosβ=3/5
因为sin^2(α)+cos^2(α)=1且α,β∈[0,π/2],
所以cosα=12/13 sinβ=4/5
cos(α+β)=cosαcosβ-sinαsinβ=12/65