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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