Question

How do you find the amplitude, period and phase shift for `y=cos3(theta-pi)-4`?

Answer 1

See below:

Explanation:

Sine and Cosine functions have the general form of

`f(x)=aCosb(x-c)+d`

Where `a` gives the amplitude, `b` is involved with the period, `c` gives the horizontal translation (which I assume is phase shift) and `d` gives the vertical translation of the function.

In this case, the amplitude of the function is still 1 as we have no number before `cos`.

The period is not directly given by `b` , rather it is given by the equation:
Period`=((2pi)/b)`
Note- in the case of `tan` functions you use `pi` instead of `2pi`.

`b=3` in this case, so the period is `(2pi)/3`

and `c=3 times pi` so your phase shift is `3pi` units shifted to the left.

Also as `d=-4` this is the principal axis of the function, i.e the function revolves around `y=-4`