Question

函数y=f（x）=Asin（wx+b),(A>0,4>w>0,0

Answer 1

由图可得

A = 2

当x=0时,y=√3 即

√3 = 2sinb sinb = √3/2

b = π/3 或 2π/3

当y=0时,x=2π/9 即

2sin(2πw/9+b) = 0

sin(2πw/9+b) = 0

2πw/9+b = π 或 2πw/9+b = 2π

w = (9π-9b)/(2π) 或 w = (18π-9b)/(2π)

解 w = (9π-9b)/(2π) 可得

当b = π/3 时,w = 3 当b = 2π/3 时,w = 3/2

解 w = (18π-9b)/(2π) 可得

当b = π/3 时,w = 15/2 当b = 2π/3 时,w = 6

因为 4>w>0 所以w = 15/2 和 6不是解

综上可得

A = 2, b = π/3, w = 3 或

A = 2, b = 2π/3, w = 3/2