How do you simplify #cos (theta – 2pi)#?

1 Answer
mason m
Jan 31, 2016

#cos(theta)#

Explanation:

Use the cosine angle subtraction formula:

#cos(alpha-beta)=cos(alpha)cos(beta)+sin(alpha)sin(beta)#

When applied to #cos(theta-2pi)#, we get

#cos(theta-2pi)=cos(theta)cos(2pi)+sin(theta)sin(2pi)#

Simplify, knowing that #cos(2pi)=1# and #sin(2pi)=0#.

#cos(theta-2pi)=cos(theta)xx1+sin(theta)xx0#

#cos(theta-2pi)=cos(theta)#

This should make sense. Since #2pi# is one revolution around the unit circle, the angles #theta# and #theta-2pi# are in the exact same locations, so #cos(theta)=cos(theta-2pi)#.

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