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General Solutions of Trigonometric Equations

Lesson · Beginner

Trigonometry

sin⁡α=sin⁡β⇒α=β+360∘k, 180∘−β+360∘k,k∈Zcos⁡α=cos⁡β⇒α=±β+360∘k,k∈Ztan⁡α=tan⁡β⇒α=β+180∘k,k∈Zcot⁡α=cot⁡β⇒α=β+180∘k,k∈Z \begin{aligned} \sin\alpha=\sin\beta &\Rightarrow \alpha=\beta+360^\circ k,\ 180^\circ-\beta+360^\circ k, \quad k\in\mathbb Z \\[12pt] \cos\alpha=\cos\beta &\Rightarrow \alpha=\pm\beta+360^\circ k, \quad k\in\mathbb Z \\[12pt] \tan\alpha=\tan\beta &\Rightarrow \alpha=\beta+180^\circ k, \quad k\in\mathbb Z \\[12pt] \cot\alpha=\cot\beta &\Rightarrow \alpha=\beta+180^\circ k, \quad k\in\mathbb Z \end{aligned}
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