Trigonometry Definition Math Sheet

An Engineers Quick Trigonometry Definition Reference

Trig Definition Math Help

Right Triangle Definition

To define the trigonometric functions of an angle theta assign one of the angles in a right triangle that value. The functions sine, cosine, and tangent can all be defined by using properties of a right triangle. A right triangle has one angle that is 90 degrees. The longest side of the triangle is the hypotenuse. The side opposite theta will be referred to as opposite. The other side next to theta will be referred to as adjacent. The following properties exist:

Sine Definition

definition of the sine function

Cosine Definition

definition of the cosine function

Tangent Definition

definition of the tangent function

Cosecant Definition

definition of the cosecant function

Secant Definition

definition of the secant function

Cotangent Definition

definition of the cotangent function

Unit Circle Definition

unit circle definition for sine

unit circle definition for cosine

unit circle definition for tangent

unit circle definition for cosecant

unit circle definition for secant

unit cirle definition for cotangent

Properties of Trig Functions


The possible angle input for each function is defined below:

domain of sine function

domain of cosine function

domain of tangent function

domain of cosecant function

domain of secant function

domain of cotanent function


The ranges of values possible for each of these functions are:

range of sine function

range of cosine function

range of tangent function

range of cosecant function

range of secant function

range of cotangent function


The periods for each of these trig functions are:

period of sine function

period of cosine function

period of tangent function

period of cosecant function

period of secant function

period of cotangent function

Inverse Trig Functions

Definition of Inverse Trig Functions

The definitions of the inverse trig functions are:

definition of inverse sine

definition of inverse cosine

definition of inverse tangent

Inverse Trig functions are also notated as:

inverse notation of asin

inverse notation of acos

inverse notation of atan

Domain of Inverse Trig Functions

domain of inverse sin

domain of inverse cosine

domain of inverse tangent

Range of Inverse Trig Functions

range of inverse sin

range of inverse cosine

range of inverse tangent

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