Chapter 7 Trigonometric Identities and Equations

7.1 BASIC TRIGONOMETRIC IDENTITIES

Reciprocal Identities

Quotient Identities

Pythagorean Identities

Opposite Angle Identities sin [-A] = -sin A cos [-A] = cos A

7.2 VERIFYING TRIGONOMETRIC IDENTITIES

Tips For Verifying Trig Identities Simplify the complicated side of the equation Use your basic trig identities to substitute parts of the equation Factor/Multiply to simplify expressions Try multiplying expressions by another expression equal to 1 REMEMBER to express all trig functions in terms of SINE AND COSINE

7.3 SUM AND DIFFERENCE IDENTITIES

Difference Identity for Cosine Cos (a – b) = cosacosb + sinasinb As illustrated by the textbook, the difference identity is derived by using the Law of Cosines and the distance formula

Sum Identity for Cosine Cos (a + b) = cos (a - (-b)) The sum identity is found by replacing -b with b *Note* If a and b represent the measures of 2 angles then the following identities apply: cos (a ± b) = cosacosb ± sinasinb

Sum/Difference Identity For Sine sinacosb + cosasinb = sin(a + b) – sum identity for sine If you replace b with (-b) you can get the difference identity of sine. sin (a – b) = sinacosb - cosasinb

Sum & Difference