Trigonometric Ratios
- Formula / Rule
- Trigonometric Ratios
- Topic
- Trigonometry
- Formula
In a right-angled triangle (angle $\theta$):
Ratios:
- $\text{sin } \theta = \text{Opposite} / \text{Hypotenuse}$
- $\text{cos } \theta = \text{Adjacent} / \text{Hypotenuse}$
- $\text{tan } \theta = \text{Opposite} / \text{Adjacent} = \text{sin } \theta / \text{cos } \theta$
- $\text{cosec } \theta = 1/\text{sin } \theta$
- $\text{sec } \theta = 1/\text{cos } \theta$
- $\text{cot } \theta = 1/\text{tan } \theta$
Standard Values:
$\theta$ sin cos tan 0° 0 1 0 30° 1/2 $\sqrt{3}/2$ $1/\sqrt{3}$ 45° $1/\sqrt{2}$ $1/\sqrt{2}$ 1 60° $\sqrt{3}/2$ 1/2 $\sqrt{3}$ 90° 1 0 $\infty$ - When to Use
- Height and distance problems, right-angle triangle calculations.
- Worked Example
Q: A ladder 10 m long leans against a wall at 60°. Height reached?
Height $= 10 \times \text{sin } 60° = 10 \times (\sqrt{3}/2) = \textbf{5\sqrt{3} \approx 8.66 m}$