f(x)=1/3sin(2/3x-π/4)+4

Find the amplitude, period, phase shift, and vertical shift of the function.
Amplitude:1/3
Period:??????
Phase Shift:???????
Vertical Shift:+4
Please Help ?

see links below, sorry I tried your problem but couldn't figure it out

To find the period of the function f(x) = (1/3)sin((2/3)x-π/4)+4, we need to look at the coefficient in front of the x. In this case, it is (2/3).

The period of a general sine function f(x) = a*sin(b(x-c)) + d is given by the formula 2π/|b|.

Therefore, the period of f(x) = (1/3)sin((2/3)x-π/4)+4 is 2π/|(2/3)|, which simplifies to (2π*3)/2, or 3π.

To find the phase shift of the function, we need to look at the value inside the sine function: (2/3)x-π/4. The phase shift is given by the formula c in the general form f(x) = a*sin(b(x-c)) + d. In this case, c is equal to π/4.

For the vertical shift, we look at the constant term at the end of the function. In this case, it is +4, so the vertical shift is +4.

To summarize:
Amplitude: 1/3
Period: 3π
Phase Shift: π/4
Vertical Shift: +4