Trigonometry
Unit Circle
The length of the blue line is the sine of the angle θ.
Trigonometric Ratios of Specific Angles
| \(0^\circ\) | \(30^\circ\) | \(45^\circ\) | \(60^\circ\) | \(90^\circ\) | |
| \(\sin\) | \( 0 \) | \( \frac{1}{2} \) | \( \frac{1}{\sqrt2} \) | \( \frac{\sqrt3}{2} \) | \( 1\) |
|---|---|---|---|---|---|
| \(\cos\) | \( 1\) | \( \frac{\sqrt3}{2} \) | \( \frac{1}{\sqrt2} \) | \( \frac{1}{2} \) | \( 0 \) |
| \(\tan\) | \(0\) | \(\frac{1}{\sqrt3}\) | \(1\) | \(\sqrt3\) | \(\text{n.d}\) |
| \(\cosec\) | \(\text{n.d}\) | \(2\) | \(\sqrt2\) | \(\frac{2}{\sqrt3}\) | \(1\) |
| \(\sec\) | \(1\) | \(\frac{2}{\sqrt3}\) | \(\sqrt2\) | \(2\) | \(\text{n.d}\) |
| \(\cot\) | \(\text{n.d}\) | \(\sqrt3\) | \(1\) | \(\frac{1}{\sqrt3}\) | \(0\) |
Trigonometric Identities
- \(\sin^2\theta + \cos^2\theta = 1\)
- \(1 + \tan^2\theta = \sec^2\theta\)
- \(1 + \cot^2\theta = \cosec^2\theta\)