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$\begin{aligned} \sin (-\theta) &= - \sin \theta &&- (1) \\ \tan (-\theta) &= - \tan \theta &&- (2) \\ \cos (-\theta) &= \cos \theta &&- (3) \\ \sin (\frac{\pi}{2} -\theta) &= \cos\theta &&- (4) \\ \cos(\frac{\pi}{2}-\theta) &= \sin\theta &&- (5) \\ \tan (\frac{\pi}{2}-\theta) &= \cot \theta &&- (6) \\ \sin^2 \theta + \cos^2 \theta &= 1 &&- (7) \\ 1 + \cot^2 \theta &= \csc^2 \theta &&- (8) \\ 1 + \tan^2 \theta &= \sec^2 \theta &&- (9) \end{aligned}$

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