471 7 A Look Back Chapter 5 introduced inverse functions and developed their properties, particularly the relationship between the domain and range of a function and those of its inverse. We learned that only one-to-one functions have inverse relations that are also functions. However, sometimes an appropriate restriction on the domain of a function that is not one-to-one yields a new function that is one-to-one. Then the function defined on the restricted domain has an inverse function. Also, we saw that the graphs of a function and its inverse are symmetric with respect to the line = y x. Chapter 5 continued by defining two transcendental functions: the exponential function and the inverse of the exponential function, the logarithmic function. Chapter 6 defined six more transcendental functions, the trigonometric functions, and discussed their properties. A Look Ahead The first two sections of this chapter define the six inverse trigonometric functions and investigate their properties. Section 7.3 discusses equations that contain trigonometric functions. Sections 7.4 through 7.7 continue the derivation of identities. These identities play an important role in calculus, the physical and life sciences, and economics, where they are used to simplify complicated expressions. Outline 7. 1 The Inverse Sine, Cosine, and Tangent Functions 7. 2 The Inverse Trigonometric Functions (Continued) 7. 3 Trigonometric Equations 7. 4 Trigonometric Identities 7. 5 Sum and Difference Formulas 7. 6 Double-angle and Half-angle Formulas 7. 7 Product-to-Sum and Sum-to-Product Formulas Chapter Review Chapter Test Cumulative Review Chapter Project Analytic Trigonometry Mapping Your Mind The ability to organize material in your mind is key to understanding. You have been exposed to a lot of concepts at this point in the course, and it is a worthwhile exercise to organize the material. In the past, we might organize material using index cards or an outline. But in today’s digital world, we can use interesting software that enables us to digitally organize the material that is in our mind and share it with anyone on the Web. —See the Internet-based Chapter Project — Credit: maxkabakov/123RF
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