Question

How do you find the amplitude, period, vertical and phase shift and graph `y=3+1/2cos(theta+pi)`?

Answer 1

• amplitude `=1/2`

• period `=2 pi`

• vertical shift `=+3`

• phase shift `=-pi`

Explanation:

`y=3+1/2cos(theta+pi)`

maybe start by re-writing it as

`y-3 = 1/2cos(theta+pi)`

So:

y is shifted up by 3, the vertical shift, and `theta` is shifted left by `pi`

`implies Y = 1/2cos(Theta)`, where `Y = y - 3, Theta = theta + pi`, and the function `cos(Theta)` has period `2 pi` and `1/2cos(Theta)` has amplitude `1/2`.

We conclude that:

• amplitude `=1/2`

• period `=2 pi`

• vertical shift `=+3`

• phase shift `=-pi`