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.

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