已知函数f(x)=2sin(3分之1—6分之π),x∈R,(1)求f(0)的值;(2)设α,β∈0,2分之π,f(3α+2分之π)=13分之10,f(3β+2π)=5分之6,求sin(α+β)的值

Question

已知函数f(x)=2sin(3分之1—6分之π),x∈R,(1)求f(0)的值;
(2)设α,β∈【0,2分之π】,f(3α+2分之π)=13分之10,f(3β+2π)=5分之6,求sin(α+β)的值

Answer 1

f(x)=2sin(x/3-π/6),(1)求f(0)的值;f(0)=-1,f(3α+π/2)=10/13 ,f(3β+2π)=6/5,f(3α+π/2)=2sin[1/3(3α+π/2)-π/6]=2sinα=10/13. sinα=5/13, cosα=12/13f(3β+2π)=2sin[1/3(3β+2π)-π/6]=2sin(β+π/2)=2...