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

1 Answer
Joshua Z.
Nov 23, 2017

y=cos(x+pi)

Explanation:

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

y=cos(x-b)

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(x-(-pi))

y=cos(x+pi)

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, (0,1), has been translated to the left pi units, to (-pi, 1). Hope this helps!

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