tailieunhanh - Ebook Precalculus mathematics for calculus (7th edition): Part 2

(BQ) Part 2 book "Precalculus mathematics for calculus" has contents: Analytic trigonometry; polar coordinates and parametric equations, vectors in two and three dimensions, systems of equations and inequalities, conic sections, sequences and series, limits - A preview of calculus. | 7 Trigonometric Identities Addition and Subtraction Formulas Double-Angle, Half-Angle, and Product-Sum Formulas Basic Trigonometric Equations More Trigonometric Equations Focus on Modeling  Traveling and Standing Waves © Jule_Berlin/ Analytic Trigonometry In Chapters 5 and 6 we studied graphical and geometric properties of the trigonometric functions. In this chapter we study algebraic properties of these functions, that is, simplifying and factoring expressions and solving equations that involve trigonometric functions. We have used the trigonometric functions to model different real-world phenomena, including periodic motion (such as the sound waves produced by a band). To obtain information from a model, we often need to solve equations. If the model involves trigonometric functions, we need to solve trigonometric equations. Solving trigonometric equations often involves using trigonometric identities. We’ve already encountered some basic trigonometric identities in the preceding chapters. We begin this chapter by finding many new identities. 537 Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 538  CHAPTER 7  ■  Analytic Trigonometry   Trigonometric Identities ■  Simplifying Trigonometric Expressions  ■  Proving Trigonometric Identities Recall that an equation is a statement that two mathematical expressions are equal. For example, the following are equations: 1 x 12 2 x 2 2x 1 x 2 5 sin2 t cos2 t 1 An identity is an equation that is true for all .