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Chapter 7 Trigonometric Identities and Equations

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7.1 BASIC TRIGONOMETRIC IDENTITIES

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Reciprocal Identities

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Quotient Identities

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Pythagorean Identities

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

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7.2 VERIFYING TRIGONOMETRIC IDENTITIES

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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

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7.3 SUM AND DIFFERENCE IDENTITIES

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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

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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

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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

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Sum & Difference

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