Sine and Cosine

Middle School

Definition

In a right triangle, sine (sin) is the ratio of opposite/hypotenuse, and cosine (cos) is adjacent/hypotenuse. On the unit circle, for angle θ, the point coordinates are (cos θ, sin θ).

Formulas

sin θ = (opposite)/(hypotenuse)

Definition of sine (right triangle)

cos θ = (adjacent)/(hypotenuse)

Definition of cosine (right triangle)

sin² θ + cos² θ = 1

Pythagorean identity

Examples

Example 1

Find sin θ and cos θ when θ = 30°.

Example 2

If sin θ = 3/5, find cos θ (0° < θ < 90°).

History

Discovered by: Hipparchus (c. 190-120 BCE)

Ancient Greek astronomer Hipparchus established the foundations of trigonometry.

Applications

Physics

Wave, oscillation, rotation analysis

Engineering

Signal processing, circuit design

Computer Graphics

Rotation transforms, animation