CHAPTER 7 - Analytic Trigonometry

Abstract

This chapter presents analytic trigonometry. A trigonometric identity is true for all values of the variable, whereas a trigonometric equation is true for only some values of the variable. Trigonometric identities are useful for two reasons: (1) for simplifying expressions and (2) for verifying other identities. Two angles whose sum is 90 (π/2) are called complementary angles. The sine of an acute angle α is equal to the cosine of its complement, that is, sin α = cos (90 − α); similarly, cos α = sin (90 − α) and tan α = cot (90 − α). Functions satisfying this basic concept are called cofunctions. The secant and cosecant is another pair of cofunctions. There are eight product–sum formulas in analytic trigonometry. A trigonometric equation is an equation involving a trigonometric function. Because of the periodic nature of the trigonometric functions, if a trigonometric equation has a solution, it will have an infinite number of solutions. This is generally resolved by seeking the solutions only for values of the variable between 0 and 2π.