math

Trigonometric Functions — Formulas, Graphs, Values

The six trigonometric functions — sine, cosine, tangent, cosecant, secant, and cotangent — turn angles into ratios. Sine and cosine are read from the y- and x-coordinates of a point on the unit circle; tangent is their ratio; the other three are reciprocals. All six are periodic, defined for most real angles, and form the foundation of trig identities, calculus, and wave physics.

Trigonometric

math

Pythagorean Identities — Formulas, Proof, Examples

The three Pythagorean identities — sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = csc²θ — are the load-bearing equations of trigonometry. All three come from one geometric fact: every point on the unit circle satisfies x² + y² = 1. Once you know the first, the other two follow by dividing through by cos²θ and sin²θ.

Trigonometric