| Pythagorean Identities |
| \( \sin^2 \theta + \cos^2 \theta = 1 \) |
| \( \tan^2 \theta + 1 = \sec^2 \theta \) |
| \( \cot^2 \theta + 1 = \csc^2 \theta \) |
| Double Angle Formulas |
| \( \sin (2 \theta) = 2 \sin \theta \cos \theta \) |
| \( \cos (2 \theta) = \cos^2 \theta - \sin^2 \theta \) |
| \( \cos (2 \theta) \) \( = 2 \cos^2 \theta - 1 \) |
| \( \cos (2 \theta) \) \( = 1 - 2 \sin^2 \theta \) |
| \( \tan (2 \theta) = {2 \tan \theta \over 1 - \tan^2 \theta } \) |
| Half Angle Formulas |
| \( \sin^2 \theta = \frac{1}{2} (1 - \cos (2 \theta)) \) |
| \( \cos^2 \theta = \frac{1}{2} (1 + \cos (2 \theta)) \) |
| \( \tan^2 \theta = {1 - \cos (2 \theta) \over 1 + \cos (2 \theta) } \) |
| Sum & Difference Formulas |
| \( \sin (\alpha \pm \beta) = \sin \alpha \cos \beta \pm \cos \alpha \sin \beta \) | \( \cos (\alpha \pm \beta) = \cos \alpha \cos \beta \mp \sin \alpha \sin \beta \) |
| \( \tan (\alpha \pm \beta) = {\tan \alpha \pm \tan \beta \over 1 \mp \tan \alpha \tan \beta} \) |
| Product to Sum Formulas |
| \( \sin \alpha \sin \beta = \frac{1}{2} [\cos (\alpha - \beta) - \cos (\alpha + \beta)] \) |
| \( \cos \alpha \cos \beta = \frac{1}{2} [\cos (\alpha - \beta) + \cos (\alpha + \beta)] \) |
| \( \sin \alpha \cos \beta = \frac{1}{2} [\sin (\alpha + \beta) + \sin (\alpha - \beta)] \) |
| \( \cos \alpha \sin \beta = \frac{1}{2} [\sin (\alpha + \beta) - \sin (\alpha - \beta)] \) |
| Sum to Product Formulas |
| \( \sin \alpha + \sin \beta = 2 \sin ({\alpha + \beta \over 2}) \cos ({\alpha + \beta \over 2}) \) |
| \( \sin \alpha - \sin \beta = 2 \cos ({\alpha + \beta \over 2}) \sin ({\alpha + \beta \over 2}) \) |
| \( \cos \alpha + \cos \beta = 2 \cos ({\alpha + \beta \over 2}) \cos ({\alpha + \beta \over 2}) \) |
| \( \cos \alpha - \cos \beta = -2 \sin ({\alpha + \beta \over 2}) \sin ({\alpha + \beta \over 2}) \) |
| \( \sin (\frac{\pi}{2} - \theta) = \cos \theta \) | \( \cos (\frac{\pi}{2} - \theta) = \sin \theta \) |
| \( \sec (\frac{\pi}{2} - \theta) = \csc \theta \) | \( \csc (\frac{\pi}{2} - \theta) = \sec \theta \) |
| \( \tan (\frac{\pi}{2} - \theta) = \cot \theta \) | \( \cot (\frac{\pi}{2} - \theta) = \tan \theta \) |
| \( \sin (\theta + 2 \pi n) = \sin \theta \) | \( \csc (\theta + 2 \pi n) = \csc \theta \) |
| \( \cos (\theta + 2 \pi n) = \cos \theta \) | \( \sec (\theta + 2 \pi n) = \sec \theta \) |
| \( \tan (\theta + \pi n) = \tan \theta \) | \( \cot (\theta + \pi n) = \cot \theta \) |
| \( \sin (-\theta) = -\sin \theta \) | \( \csc (-\theta) = -\csc \theta \) |
| \( \cos (-\theta) = \cos \theta \) | \( \sec (-\theta) = \sec \theta \) |
| \( \tan (-\theta) = -\tan \theta \) | \( \cot (-\theta) = -\cot \theta \) |
| \( \sin (\pi - \theta) = \sin \theta \) | \( \cos (\pi - \theta) = -\cos \theta \) |
| \( \tan \theta = {\sin \theta \over \cos \theta}\) |
| \( \cot \theta = {\cos \theta \over \sin \theta}\) |