This table presents key relationships between the fundamental trigonometric functions \(\sin \alpha\), \(\cos \alpha\), \(\tan \alpha\), and \(\cot \alpha\). Understanding these relationships helps in simplifying expressions and solving trigonometric equations.
| sin α | cos α | tan α | cot α | |
|---|---|---|---|---|
| sin α | ± \(\sqrt{1 - \cos^2 \alpha}\) | ± \(\frac{\tan \alpha}{\sqrt{1 + \tan^2 \alpha}}\) | ± \(\frac{1}{\sqrt{1 + \cot^2 \alpha}}\) | |
| cos α | ± \(\sqrt{1 - \sin^2 \alpha}\) | ± \(\frac{1}{\sqrt{1 + \tan^2 \alpha}}\) | \(\cot \alpha \tan \alpha\) | |
| tan α | \(\frac{\sin \alpha}{\sqrt{1 - \sin^2 \alpha}}\) | ± \(\frac{\sqrt{1 - \cos^2 \alpha}}{\cos \alpha}\) | \(\frac{1}{\tan \alpha}\) | |
| cot α | ± \(\frac{\sqrt{1 - \sin^2 \alpha}}{\sin \alpha}\) | \(\frac{\cos \alpha}{\pm \sqrt{1 - \cos^2 \alpha}}\) | \(\frac{1}{\tan \alpha}\) |