Chapter 7 introduces the concept of trigonometric identities—true statements that are applied to simplify and verify trigonometric expressions and statements. In this chapter, you explore more advanced trigonometric identities, including double-angle, half-angle, power-reducing, product-to-sum, and sum-to-product formulas. Most of the identities in Chapters 7 and 8 are expressed in terms of sine and cosine, but the final section of this chapter explores identities involving the tangent function.
Chapter 7 dealt with trig expressions containing “x.” (Remember, x is called the “argument” of the expression cos x.) This chapter deals with more complicated arguments, like cos 2x and sin x/2.
Don’t start this chapter unless you’ve already finished Chapter 7, because you’ll see some of those single-angle identities seep through into these problems. Focus your attention on the first and last sections of this chapter (double angles and tangent identities). The rest of the sections discuss identities that are used much less frequently—they each have a particular niche that makes them useful only in very specific circumstances.