Question

How do you find the amplitude, period, and shift for `y=sin (3x-pi/4)`?

Answer 1

`Amplitude =1`
`Period=(2pi)/3`
phase (shift) `= pi/4` to the right

Explanation:

Let `y=asin(bx+c)`
The amplitude is the coefficient `a` of the sine, here it is 1
The period depends on the coefficient b of x, So here we have `3`
So the peroid `=(2pi)/3`, if the coefficient was 1, the period is `2pi`
The phase shift depends on the value and sign of c: Here it is `-pi/4` So it is `pi/4` to the right