1. Trigonometric identities:
\(Sin^2\theta+cos^2\theta = 1\)
\(1+ tan^2\theta = sec^2\theta\)
\(1+ cot^2\theta = cosec^2\theta\)
\(Sin^2\theta+cos^2\theta = 1\)
\(1+ tan^2\theta = sec^2\theta\)
\(1+ cot^2\theta = cosec^2\theta\)
2. Trigonometric ratios:
| \(sin \theta = \frac{opposite\ side}{hypotenus}\) | \(cosec \theta = \frac{hypotenus}{opposite\ side}\) |
| \(cos \theta = \frac{Adjacent\ side}{hypotenus}\) | \(sec \theta = \frac{opposite\ side}{Adjacent\ side}\) |
| \(tan \theta = \frac{opposite\ side}{Adjacent\ side}\) | \(cot \theta = \frac {Adjacent\ side}{opposite\ side}\) |
3. Reciprocal of trigonometry:
| \(sin \theta = \frac{1}{cosec\theta}\) | \(cosec\theta = \frac{1}{sin\theta}\) |
| \(cos\theta = \frac{1}{sec\theta}\) | \(sec\theta = \frac{1}{cos\theta}\) |
| \(tan\theta = \frac{1}{cot\theta}\) | \(cot\theta = \frac {1}{tan\theta}\) |
| \(tan\theta = \frac{sin\theta}{cos\theta}\) | \(cot\theta = \frac{cos\theta}{sin\theta}\) |
| \(tan\theta = \frac{sec\theta}{cosec\theta}\) | \(cot\theta = \frac{cosec\theta}{sec\theta}\) |
4. Velues of trigonometric ratios:
|
Trignometric ratio
|
0° | 30° | 45° | 60° | 90° |
| \(sin \theta\) | \(0\) | \(\frac{1}{2}\) | \(\frac{1}{\sqrt{2}}\) | \(\frac{\sqrt{3}}{2}\) | \(1\) |
| \(cos \theta\) | \(1\) | \(\frac{\sqrt{3}}{2}\) | \(\frac{1}{\sqrt{2}}\) | \(\frac{1}{2}\) | \(0\) |
| \(tan \theta\) | \(0\) | \(\frac{1}{\sqrt{3}}\) | \(1\) | \(\sqrt{3}\) | not defined |
| \(cot \theta\) | not defined | \(2\) | \(\sqrt{2}\) | \(\frac{2}{\sqrt{3}}\) | \(1\) |
| \(sec \theta\) | \(1\) | \(\frac{2}{\sqrt{3}}\) | \(\sqrt{2}\) | \(2\) | not defined |
| \(cosec \theta\) | not defined | \(\sqrt{3}\) | \(1\) | \(\frac{1}{\sqrt{3}}\) | \(0\) |