Opposite arcs

Property — Opposite arcs: $-\alpha$

$\sin(-\alpha) = -\sin\alpha,\qquad \cos(-\alpha) = \cos\alpha,\qquad \tan(-\alpha) = -\tan\alpha.$ Geometrically: the point $P_{-\alpha}$ is the mirror image of $P_\alpha$ about the $x$-axis. Abscissa unchanged, ordinate with its sign reversed.

These formulae express the fact that $\cos$ is an even function and $\sin$ (like $\tan$) is odd.

Links

Topics: Trigonometry
Concepts: Associated arcs · Cosine · Sine · Tangent
Functions: Cosine · Sine · Tangent
Skills: Using formulae