Equalities that involve trigonometric functions and are true for every single value of the variables that are defined. These functions are useful when a problem with a trig function must be simplified

There are 3 main types of identities : Basic, Pythagorean and Sum and difference

Trigonometric Functions

A function of an angle, or of an abstract quantity, used in trigonometry, including the sine, cosine, tangent, cotangent, secant, and cosecant, and their hyperbolic counterparts.

When dealing with Trigonometric Functions we must keep in mind the angles of the triangle and their ratios

The definitions of the six functions and the Pythagorean Theorem provide a powerful means of finding unknown sides and angles. For any right triangle, if the measures of one side and either another side or angle are known, the measures of the other sides and angles can be determined.

Unit Circle

The unit circle is used to understand sines and cosines of angles found in right triangles. The unit circle has a center at the origin (0,0) and a radius of one unit. Angles are measured starting from the positive x-axis in quadrant I and continue around the unit circle. The ray from the origin to a point on the circle (x,y) will give the trigonometric functions of the angle through the coordinates.

The definition of the trigonometric functions cosine and sine in terms the coordinates of points lying on the unit circle immediately gives us the fact often known as the fundamental trigonometric identity.