# How do you graph  y=4cos2(x-pi)+1?

Nov 29, 2016

The graph is a cosine wave about y = 1, with amplitude = 4, period = $\pi$. The graph is inserted.

#### Explanation:

$y - 1 = 4 \cos x \left(x - \pi\right) = 4 \cos \left(2 x - 2 \pi\right) = 4 \cos \left(2 \pi - 2 x\right) = 4 \cos 2 x$.

This represents a cosine wave about y - 1. The period is $\frac{2 \pi}{2} = \pi$

and the amplitude about y = 1 is 4.

Graph is inserted. Here, $\pi = 3.14$, nearly. Look for graph for one

period with $\in \left[- \frac{\pi}{2} , \frac{\pi}{2}\right] = \left[- 1.57 , 1.57\right]$ Correspondingly, y reaching

crest y = 5 twice and minimum y =-3 also twice at the ends.

graph{y-1-4cos(2x)=0 [-10, 10, -5, 5]}