Right Triangle Trigonometry Definitions

Given triangle ABC,

There are six possible side ratios named: Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent.

The Pythagorean theorem applies,

Special 30-60-90 triangle:

Special 45-45-90 triangle:

Special Trig Function Values:

Pythagorean triples (primitives) with c ≤ 100:

Note: (6, 8, 10) is not a primitive because it is a multiple of (3, 4, 5).

Trigonometric functions of special angles in classic table form:

Other Inverse Functions

Inverse Cosecant Function (y = arccsc x)

 
Inverse Secant Function (y = arcsec x)

 
Inverse Cotangent Function (y = arccot x)

Graphing Cosecant, Secant, and Cotangent

Reciprocal relationships

One cycle of cosecant: period 2π

One cycle of secant: period 2π

One cycle of cotangent: period π