Question

How do I find the phase shift of a sinusoidal graph?

Answer 1

Find the value of `x` at which we find `sin(0)`.

Explanation:

Examples:

`y=3+2sin(3x- pi/4)`

Solve: `3x-pi/4 = 0`

So `x= pi/12` is the shift.

`y=5-sin(4x+ pi/2)`

Solve: `4x + pi/2 = 0`

So `x= -pi/8` is the shift.

`y=-3sin(pix+ (3pi)/4)`

Solve: `pix + (3pi)/4 = 0`

So `x= -3/4` is the shift.

Some textbooks use:
`y = asin(bx+c)` has phase shift `-c/b`

Other textbooks use:
`y = asin(bx-c)` has phase shift `c/b`

For me (having taught out of both kinds of textbook), it's easier just to solve the equation.