College Algebra & Trigonometry, 2018a

Chapter 10
Trigonometric Identities and
Equations
Due to the nature of the trigonometric ratios, they have some interesting properties
that make them useful in a number of mathematical problem-solving situations.
One of the hallmarks of mathematical problem-solving is to change the
appearance of the problem without changing its value. Trigonometric identities
can be very helpful in changing the appearance of a problem.
The process of demonstrating the validity of a trigonometric identity involves
changing one trigonometric expression into another, using a series of clearly defined
steps. We’ll look at a few examples briefly, but first, let’s examine some of
the fundamental trigonometric identities.
10.1 Reciprocal and Pythagorean Identities
The two most basic types of trigonometric identities are the reciprocal identities
and the Pythagorean identities. The reciprocal identities are simply definitions of
the reciprocals of the three standard trigonometric ratios:
sec θ = 1
cos θ
csc θ = 1
sin θ
cot θ = 1
tan θ
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