# How do you find the amplitude, period, vertical and phase shift and graph y=costheta+1/4?

Nov 14, 2016

#### Explanation:

For the general form

$y = A \cos \left(B \theta + C\right) + D$

The amplitude is A
The period is, $\tau = \frac{2 \pi}{B}$
The phase shift is, $\theta = \frac{C}{B}$
The vertical shift is D

Matching the above to the given equation $y = \cos \left(\theta\right) + \frac{1}{4}$:

The amplitude is 1
The period is $\tau = \frac{2 \pi}{1} = 2 \pi$
The phase shift is, $\theta = \frac{0}{1} = 0$
The vertical shift is 1/4