How do you evaluate #cos^2 (-135)#?

1 Answer
Mar 22, 2016

#cos^2(-135^o)=1/2#

Explanation:

First of all, we should assume that #-135# is degrees, not radians.

Secondly, recall the definition of a function cosine.
Cosine of an angle is an abscissa (X-coordinate) of the point on a unit circle at the end of a radius that makes this angle in the counterclockwise direction from the positive direction of X-axis.
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From this definition and, as seen from the picture, it is obvious that #cos(x)=cos(-x)# and
#cos(180^o-x)=-cos(x)#

Let's now find the value of #cos(-135^o)#.
From #cos(-x)=cos(x)# follows that
#cos(-135^o)=cos(135^o)#

From #cos(180^o-x)=-cos(x)# follows that
#cos(135^o)=cos(180^o-45^o)=-cos(45^o)=-sqrt(2)/2#

Hence, #cos^2(-135^o)=(-sqrt(2)/2)^2 = 1/2#