Question

求一个函数解答题

已知函数f(x)=Asin(x+φ),(A＞0,0＜φ＜π),x∈R的最大值是2,其图像经过点M(π/3,1)
(1).求f(x)的解析式;
(2).若tanα=3,且函数g(x)=f(x+α)+f(x+α-π/2),(x∈R)的图像关于直线x=x0对称,求tanx0的值

Answer 1

最大值是2，说明A=2，因为过M点所以
1=2sin(π/3+φ)
π/3+φ=5π/6
φ=π/2
f(x)=2sinx(x+π/2)=2cosx

2 g(x)=cos(x+a)+cos(x+a-π/2)
=cos(x+a)+sin(x+a)
=(根号2)sin(x+a-π/4)
所以x0=π/4 -a
tanx0=(tanπ/4-tana)/(1+tanπ/4tana)
=(1-3)/(1+3)=-1/2

Answer 2

f(x)=2sin(x+π/3)