# How do you use the amplitude and period to graph y=cos(x°+45°)-1?

May 21, 2016

Amplitude is $1$ and period is $2 \pi$.

#### Explanation:

In a typical sine or cosine function $y = \alpha \cos \left(\beta x + \gamma\right) + \delta$,

$\alpha$ denotes amplitude,

period is $\frac{2 \pi}{\beta}$ or ${360}^{o} / \beta$

phase shift is given by $\frac{- \gamma}{\beta}$

and $\delta$ denotes vertical shift.

Hence in $\cos \left({x}^{\oplus} {45}^{o}\right) - 1$

Amplitude is $1$ and period is $2 \pi$.

graph{cos(x+pi/4) -1 [-10, 10, -5, 5]}