Sumário
- Preface
7The Unit Circle: Sine and Cosine Functions
9Trigonometric Identities and Equations
- Introduction to Trigonometric Identities and Equations
- 9.1Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions
- 9.2Sum and Difference Identities
- 9.3Double-Angle, Half-Angle, and Reduction Formulas
- 9.4Sum-to-Product and Product-to-Sum Formulas
- 9.5Solving Trigonometric Equations
11Systems of Equations and Inequalities
- AProofs, Identities, and Toolkit Functions
- Index
Key Terms
Key Terms
- double-angle formulas
- identities derived from the sum formulas for sine, cosine, and tangent in which the angles are equal
- even-odd identities
- set of equations involving trigonometric functions such that if the identity is odd, and if the identity is even
- half-angle formulas
- identities derived from the reduction formulas and used to determine half-angle values of trigonometric functions
- product-to-sum formula
- a trigonometric identity that allows the writing of a product of trigonometric functions as a sum or difference of trigonometric functions
- Pythagorean identities
- set of equations involving trigonometric functions based on the right triangle properties
- quotient identities
- pair of identities based on the fact that tangent is the ratio of sine and cosine, and cotangent is the ratio of cosine and sine
- reciprocal identities
- set of equations involving the reciprocals of basic trigonometric definitions
- reduction formulas
- identities derived from the double-angle formulas and used to reduce the power of a trigonometric function
- sum-to-product formula
- a trigonometric identity that allows, by using substitution, the writing of a sum of trigonometric functions as a product of trigonometric functions