What is the graph of #y=cos^2 x#?

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Mar 22, 2015

Here is the graph:
graph{y=(cosx)^2 [-10, 10, -5, 5]}

Remember the double-angle formula for cosine:
#cos(2x) = 2cos^2(x) -1#

Add one to both sides:
#cos (2x) + 1 = 2cos^2(x)#

Divide both sides by two:
#1/2cos(2x) +1/2 = cos^2(x)#

You now have a standard cosine equation with
Amplitude = #1/2#

Period = #pi#

Vertical Shift = up by #1/2#

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