Trigonometry Sheet 1
Fundamental Ratios & Identities
1. Definition of Ratios (Right Triangle)
| Ratio | Formula | Ratio | Formula |
|---|---|---|---|
| sin θ | $$\frac{Opposite}{Hypotenuse}$$ | cosec θ | $$\frac{Hypotenuse}{Opposite}$$ |
| cos θ | $$\frac{Adjacent}{Hypotenuse}$$ | sec θ | $$\frac{Hypotenuse}{Adjacent}$$ |
| tan θ | $$\frac{Opposite}{Adjacent}$$ | cot θ | $$\frac{Adjacent}{Opposite}$$ |
2. Reciprocal & Quotient Formulas
All 6 Reciprocals
| $$\sin \theta = \frac{1}{\csc \theta}$$ | $$\csc \theta = \frac{1}{\sin \theta}$$ |
| $$\cos \theta = \frac{1}{\sec \theta}$$ | $$\sec \theta = \frac{1}{\cos \theta}$$ |
| $$\tan \theta = \frac{1}{\cot \theta}$$ | $$\cot \theta = \frac{1}{\tan \theta}$$ |
Quotient Identities
$$\tan \theta = \frac{\sin \theta}{\cos \theta}$$ $$\cot \theta = \frac{\cos \theta}{\sin \theta}$$
3. Pythagorean Identities
$$\sin^2 \theta + \cos^2 \theta = 1$$
$$1 + \tan^2 \theta = \sec^2 \theta$$
$$1 + \cot^2 \theta = \csc^2 \theta$$