Now that we know the definitions of the trigonometric functions, and have a clear understanding how they behave as an angle changes, we can explore the relationships that exist between them.
A trigonometric identity is an equation involving trigonometric functions that can be solved by any angle. Trigonometric identities have less to do with evaluating functions at specific angles than they have to do with relationships between functions. Eight specific trigonometric identities are fundamental. These can be used to form an infinite number of other identities. We'll take a look at the eight fundamental trigonometric identities, and then some additional identities concerning negative angles (angles in which the rotation between the initial and terminal side is clockwise). Using the identities we'll learn, we can manipulate trigonometric expressions and simplify them if they're complicated. Finally, we'll review what we know so far of trigonometry before we move on to study how to solve triangles and trigonometric equations.