Trigonometry Made Simple

Trigonometry is the study of relationships between angles and sides of triangles. It started as a practical tool for astronomy and surveying, and now it is essential in physics, engineering, computer science, and many other fields.

The Basic Functions

For a right triangle, sine is opposite/hypotenuse, cosine is adjacent/hypotenuse, and tangent is opposite/adjacent. The mnemonic SOH-CAH-TOA is the classic way to remember these ratios.

Unit Circle

The unit circle is a circle with radius 1 centered at the origin. Any point on the circle has coordinates (cos θ, sin θ). This extends trigonometric functions beyond the 0°-90° range to any angle, including negative angles and angles greater than 360°. Memorizing the unit circle values for 0°, 30°, 45°, 60°, and 90° will save you enormous amounts of time in exams.

Identities

Pythagorean identities like sin²θ + cos²θ = 1, double angle formulas like sin(2θ) = 2sinθcosθ, and sum-to-product formulas come up constantly. Keep a reference sheet handy while you learn them.

Check values with our Trigonometric Calculator and review exact values with the Unit Circle Values tool.