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Precalculus 2e

Introduction to Trigonometric Identities and Equations

Precalculus 2eIntroduction to Trigonometric Identities and Equations
A sine wave models disturbance. (credit: modification of work by Mikael Altemark, Flickr).

Chapter Outline

7.1 Simplifying and Verifying Trigonometric Identities
7.2 Sum and Difference Identities
7.3 Double-Angle, Half-Angle, and Reduction Formulas
7.4 Sum-to-Product and Product-to-Sum Formulas
7.5 Solving Trigonometric Equations
7.6 Modeling with Trigonometric Functions

Math is everywhere, even in places we might not immediately recognize. For example, mathematical relationships describe the transmission of images, light, and sound. The sinusoidal graph in the figure above models music playing on a phone, radio, or computer. Such graphs are described using trigonometric equations and functions. In this chapter, we discuss how to manipulate trigonometric equations algebraically by applying various formulas and trigonometric identities. We will also investigate some of the ways that trigonometric equations are used to model real-life phenomena.

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