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Chapter 7

Chapter 7. Trigonometric Identities and Equations. 7.1 Basic Trigonometric Identities. Reciprocal Identities. These identities are derived in this manner sin = and csc = which gives you sin =. Quotient Identities.

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Chapter 7

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  1. Chapter 7 Trigonometric Identities and Equations

  2. 7.1 Basic Trigonometric Identities

  3. Reciprocal Identities These identities are derived in this manner sin = and csc = which gives you sin =

  4. Quotient Identities If using a unit circle as reference, these identities were derived using = = tan

  5. Pythagorean Identities

  6. Opposite Angle Identities

  7. 7.2 Verifying trigonometric identities

  8. 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

  9. 7.3 Sum and difference identities

  10. 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

  11. 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

  12. 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

  13. Sum & Difference Tan[a ± b] = This identity is used as both the sum and difference identity.

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