1. $$\sin(2k\pi + \alpha) = \sin \alpha \\\\ \cos(2k\pi + \alpha) = \cos \alpha \\\\ \tan(2k\pi + \alpha) = \tan \alpha \\\\ \cot(2k\pi + \alpha) = \cot \alpha \\\\ \sec(2k\pi + \alpha) = \sec \alpha \\\\ \csc(2k\pi + \alpha) = \csc \alpha$$
2. $$\sin(\pi + \alpha) = -\sin \alpha \\\\ \cos(\pi + \alpha) = -\cos \alpha \\\\ \tan(\pi + \alpha) = \tan \alpha \\\\ \cot(\pi + \alpha) = \cot \alpha \\\\ \sec(\pi + \alpha) = -\sec \alpha \\\\ \csc(\pi + \alpha) = -\csc \alpha$$
3. $$\sin(-\alpha) = -\sin \alpha \\\\ \cos(-\alpha) = \cos \alpha \\\\ \tan(-\alpha) = -\tan \alpha \\\\ \cot(-\alpha) = -\cot \alpha \\\\ \sec(-\alpha) = \sec \alpha \\\\ \csc(-\alpha) = -\csc \alpha$$
4. $$\sin(\pi - \alpha) = \sin \alpha \\\\ \cos(\pi - \alpha) = -\cos \alpha \\\\ \tan(\pi - \alpha) = -\tan \alpha \\\\ \cot(\pi - \alpha) = -\cot \alpha \\\\ \sec(\pi - \alpha) = -\sec \alpha \\\\ \csc(\pi - \alpha) = \csc \alpha$$
5. $$\sin(\alpha - \pi) = -\sin \alpha \\\\ \cos(\alpha - \pi) = -\cos \alpha \\\\ \tan(\alpha - \pi) = \tan \alpha \\\\ \cot(\alpha - \pi) = \cot \alpha \\\\ \sec(\alpha - \pi) = -\sec \alpha \\\\ \csc(\alpha - \pi) = -\csc \alpha$$
6. $$\sin(\frac{\pi}{2} - \alpha) = -\sin \alpha \\\\ \cos(\frac{\pi}{2} - \alpha) = \cos \alpha \\\\ \tan(\frac{\pi}{2} - \alpha) = -\tan \alpha \\\\ \cot(\frac{\pi}{2} - \alpha) = -\cot \alpha \\\\ \sec(\frac{\pi}{2} - \alpha) = \sec \alpha \\\\ \csc(\frac{\pi}{2} - \alpha) = -\csc \alpha$$
7. $$\sin(\frac{\pi}{2} + \alpha) = \cos \alpha \\\\ \cos(\frac{\pi}{2} + \alpha) = −\sin \alpha \\\\ \tan(\frac{\pi}{2} + \alpha) = -\cot \alpha \\\\ \cot(\frac{\pi}{2} + \alpha) = -\tan \alpha \\\\ \sec(\frac{\pi}{2} + \alpha) = -\csc \alpha \\\\ \csc(\frac{\pi}{2} + \alpha) = \sec \alpha$$
8. $$\sin(\frac{\pi}{2} - \alpha) = \cos \alpha \\\\ \cos(\frac{\pi}{2} - \alpha) = \sin \alpha \\\\ \tan(\frac{\pi}{2} - \alpha) = \cot \alpha \\\\ \cot(\frac{\pi}{2} - \alpha) = \tan \alpha \\\\ \sec(\frac{\pi}{2} - \alpha) = \csc \alpha \\\\ \csc(\frac{\pi}{2} - \alpha) = \sec \alpha$$
9. $$\sin(\frac{3\pi}{2} + \alpha) = -\cos \alpha \\\\ \cos(\frac{3\pi}{2} + \alpha) = \sin \alpha \\\\ \tan(\frac{3\pi}{2} + \alpha) = -\cot \alpha \\\\ \cot(\frac{3\pi}{2} + \alpha) = -\tan \alpha \\\\ \sec(\frac{3\pi}{2} + \alpha) = \csc \alpha \\\\ \csc(\frac{3\pi}{2} + \alpha) = -\sec \alpha$$
10. $$\sin(\frac{3\pi}{2} - \alpha) = -\cos \alpha \\\\ \cos(\frac{3\pi}{2} - \alpha) = -\sin \alpha \\\\ \tan(\frac{3\pi}{2} - \alpha) = \cot \alpha \\\\ \cot(\frac{3\pi}{2} - \alpha) = \tan \alpha \\\\ \sec(\frac{3\pi}{2} - \alpha) = -\csc \alpha \\\\ \csc(\frac{3\pi}{2} - \alpha) = -\sec \alpha$$