Question

Which expression will give you the phase shift when the standard form is f left parenthesis x right parenthesis equals a sine left parenthesis b x plus c right parenthesis plus d?

Answer 1

`Phase\ Shift = -(c)/(b)`

Explanation:

See comment for complete question

Given

`f(x) = Asin(bx+c)+d`

Required

Determine an expression for the phase shift

`f(x) = Asin(bx+c)+d`

Factorize the expression in bracket

`f(x) = Asin(b(x+(c)/(b)))+d`

The general expression is:

`F(t) = A f(B(t - C/B)) + D`

Where:

C/B is the phase shift

By comparing the general expression with:
`f(x) = Asin(b(x+(c)/(b)))+d`

`-(C)/(B) = (c)/(b)`

Multiply both sides by -1

`(C)/(B) = -(c)/(b)`

Hence:

`Phase\ Shift = -(c)/(b)`