Question

已知函数f(x)=2sin(1/3x-π/6)，x∈R (1)求f(0)的值;

(2)设α，β∈[0,π/2],f(3α+π/2)=10/13,f(3β+π/2）=6/5.求sin(α+β)的值.

Answer 1

1.f(0)=2sin(-π/6)=2×(-1/2)=-1
2.f(3α+π/2)=2sin[1/3(3α+π/2)-π/6]=2sinα=10/13 sinα=5/13 α∈[0,π/2] cosα=12/13
f(3β+π/2)=2sin[1/3(3β+π/2)-π/6]=2sinβ=6/5 sinβ=3/5 β∈[0,π/2] cosβ=4/5
sin(α+β)=sinαcosβ+sinβcosα=5/13×4/5+12/13×3/5=56/65

Answer 2

f(3a+π/2)=2sin(1/3（3a+π/2）-π/6)=2sina=10/13，sina=5/13，cosa=12/13
f(3b+2π)=2sin(1/3（3b+2π）-π/6)=2cosb=6/5， cosb=3/5，sinb=4/5
cos(a+b）=cosa*cosb-sina*ainb=12/13*3/5-5/13*4/5=16/65
sin(α+β)=sinαcosβ+sinβcosα=5/13×4/5+12/13×3/5=56/65

Answer 3

上菁优网。以下是这题的答案网址，直接点击打开就有，有详细答案过程、考点，这题是2011年广东高考题。

http://m.jyeoo.com/math2/ques/detail/5ecd8e18-3aa4-4222-8c50-7f5bc4e260d1