Question

How do you find the amplitude, period, vertical and phase shift and graph `y=3-1/2costheta`?

Answer 1

Amplitude: `1/2`
Period: `2pi`
Vertical shift: `3`
Phase shift: `pi`

Explanation:

Given: `3 - 1/2cos(theta)`

Begin by observing that multiplication of a sinusoid by negative is a phase shift of `pi`

Using the general from,

`y = Acos(Btheta+C)+D`

The phase shift `phi = C/B`

In the given equation `B = 1`, therefore, we can rewrite the equation without a negative sign if we insert `pi` phase shift:

`pi = C/1`

`C = pi`

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

Period `T = (2pi)/B`

`T = 2pi`

The amplitude is `A = 1/2`

Vertical shift `D = 3`