# Trigonometry

Trigonometry is the study of angles and triangles, relying heavily on three basic functions: sine, cosine and tangent, and their inverses, Cotangent (Cot), Secant (sec) and Cosecant (csc). These functions are abbreviated as "sin", "cos" and "tan".

These functions are defined by reference to a "right triangle," which is a triangle in which one angle is 90 degrees.

A way to remember the relationships is the mnemonic SOH-CAH-TOA ("soak a toe"). Think of a man soaking his toe in a tub of water - preferably a three-sided tub!
• SOH: Sine = opposite over hypotenuse
• CAH: Cosine = adjacent over hypotenuse
• TOA: Tangent = opposite over adjacent

## Formulas

Complementary formulas:

$\sin(90^\circ-\alpha) \, = \, \cos\alpha$
$\cos(90^\circ-\alpha) \, = \, \sin\alpha$

Pythagorean trigonometric identity:

$\sin^2\alpha + \cos^2\alpha \, = 1$