# How do you find the amplitude, period, vertical and phase shift and graph y=costheta-5?

Jan 16, 2018

Amplitude will be $1$, the value of the coefficient of cosine.

Period will be that of a standard cosine graph, or $2 \pi$.

There will be a phase shift of $0$ because the graph has been moved neither left nor right.

There will be a vertical shift of 5 units down because the value of $d$ in $y = a \cos \left(b \left(x - c\right)\right) + d$ is $- 5$ .

The graph is as follows. It is the exact graph of $y = \cos x$ with a transformation of $5$ units down.

graph{y = cosx- 5 [-10, 10, -5, 5]}

Hopefully this helps!