Show that cos(pi - θ) = -cos θ
for every angle θ
Using the unit circle on an x-y graph, draw terminal arms with angles θ and pi-θ
These will be in quadrants I and II, let their endpoints be (x,y) and (-x,y).
from their endpoints drop lines to the x-axi, giving you two right-angles triangles that are similar.
from the first triangle:
cos θ = x/1 = x
from the second triangle:
cos(pi-θ ) = -x/1
x = -cos(pi-θ)
equating the two x's
-cos(pi-θ) = cos θ or
cos(pi-θ) = -cos θ