calculus

Show that cos(pi - θ) = -cos θ
for every angle θ

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  1. 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

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