Mathematics
Trigonometry Made Simple: sin, cos, tan Explained
A beginner-friendly guide to understanding sine, cosine, and tangent with practical examples and a reference table.
2026-05-15 6 min read
What Is Trigonometry?
Trigonometry is the branch of mathematics that studies relationships between the sides and angles of triangles. The three core functions — sine, cosine, and tangent — relate an angle to ratios of a right triangle's sides.
The Three Core Functions
For a right triangle with angle θ:
- sin(θ) = Opposite ÷ Hypotenuse
- cos(θ) = Adjacent ÷ Hypotenuse
- tan(θ) = Opposite ÷ Adjacent = sin(θ) ÷ cos(θ)
Key Reference Values
| Angle | sin | cos | tan |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 0.5 | √3/2 ≈ 0.866 | 1/√3 ≈ 0.577 |
| 45° | √2/2 ≈ 0.707 | √2/2 ≈ 0.707 | 1 |
| 60° | √3/2 ≈ 0.866 | 0.5 | √3 ≈ 1.732 |
| 90° | 1 | 0 | undefined |
Practical Example
A ladder 5 m long leans against a wall at 60°. How high does it reach?
Height = 5 × sin(60°) = 5 × 0.866 = 4.33 m
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