How do you prove the reduction identities $Cos(x+pi)= -cos(x)$ using a unit circle diagram?

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Answer 1 · 2015-08-19T19:01:24

I am not sure this little diagram is enough but...

Have a look:
enter image source here

Answer 2 · 2015-08-20T02:38:47

Supplementary arcs: sin x and $sin (x + pi)$

The trig unit circle shows the relationship between the supplementary arcs:

$sin x = sin (pi - x)$

$sin x = - sin (pi + x)$

enter image source here

How do you prove the reduction identities Cos(x+pi)= -cos(x)Cos(x+pi)= -cos(x) using a unit circle diagram?