Supplementary arcs

Property — Supplementary arcs: $\pi - \alpha$

$\sin(\pi-\alpha) = \sin\alpha,\qquad \cos(\pi-\alpha) = -\cos\alpha,\qquad \tan(\pi-\alpha) = -\tan\alpha.$ Symmetry about the $y$-axis: the point $P_{\pi-\alpha}$ has the same ordinate as $P_\alpha$ (same sine) and opposite abscissa (cosine with its sign reversed).

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