# How do you write an equation for y=cosx translated pi units to the left?

Nov 23, 2017

$y = \cos \left(x + \pi\right)$

#### Explanation:

We want to translate the graph in the x-direction, so our final equation should look like:

$y = \cos \left(x - b\right)$

Where $b$ is the number of units translated.
We are translating the graph $\pi$ units to the left, so $b$ should be equal to $- \pi$. Therefore, our final equation should look like:

$y = \cos \left(x - \left(- \pi\right)\right)$

$y = \cos \left(x + \pi\right)$

If we graph the original and translated graph, we can see the difference:

Original:
graph{cos(x) [-10, 10, -5, 5]}

Translated:
graph{y=cos(x+pi) [-10, 10, -5, 5]}

You can see the y intercept for the original equation, $\left(0 , 1\right)$, has been translated to the left $\pi$ units, to $\left(- \pi , 1\right)$. Hope this helps!