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 — $\sin^2\theta + \cos^2\theta = 1$, $1 + \tan^2\theta = \sec^2\theta$, and $1 + \cot^2\theta = \csc^2\theta$ — are the load-bearing equations of trigonometry. All three come from one geometric fact: every point on the unit circle satisfies $x^2 + y^2 = 1$. Once you know the first, the other two follow by dividing through by $\cos^2\theta$ and $\sin^2\theta$.

Trigonometric