Chapter 7 Analytic Trigonometry

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Analytic trigonometry combines trigonometric relationships with algebraic reasoning. In this chapter, you will use reciprocal, quotient, and Pythagorean identities to simplify expressions and verify identities. Addition and subtraction formulas will produce exact values for unfamiliar angles and lead naturally to double-angle, half-angle, power-reduction, and product-sum formulas. You will also study inverse trigonometric functions, their restricted domains, principal values, and compositions. The chapter concludes with trigonometric equations, where you will use unit-circle values, factoring, identities, inverse functions, periodicity, and Desmos to find exact or approximate solutions. These techniques prepare you for more advanced work in mathematics, science, and engineering.