Why is cos(pi) and cos (-pi) both equal to -1?

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Alan P. Share
Apr 22, 2015

A full circle is #2pi#

#pi# is half way around the circle counter-clockwise.

#-pi# is half way around the circle clockwise.

#cos(pi) = cos(-pi)# are the both #cos# values for the same place

They are both equal to #(-1)#
because
if viewed as a unit circle centered on the Cartesian origin
the #cos# is the #x# value
and, at halfway around the unit circle,
#x=-1#

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Mar 30, 2017

Answer:

This is what a cosine graph looks like. Since #pi# in degrees is 180, it is exactly the same distance from 0 degrees.

Explanation:

graph{cos(x) [-4.76, 4.84, -2.64, 2.16]}

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Antoine Share
Apr 22, 2015

One of the reasons is because #cos# is an even function.

This means that #costheta=cos(-theta)#

An example is the present case #cospi=cos(-pi)=-1#

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