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Efficient Verification of Trigonometric Identities

Learn how to verify trigonometric identities by following guidelines, working with one side at a time, utilizing fundamental identities, and exploring different techniques. Practice with homework exercises provided.

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Efficient Verification of Trigonometric Identities

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  1. 5.2: Verifying Trigonometric Identities

  2. Identity • An equation that is true for all real values in the domain of the variable

  3. Verify the Trigonometric Equation

  4. Guidelines for Verifying Trigonometric Identities • Work with one side of the equation at a time. It is often better to work with the more complicated side first. • Look for opportunities to factor an expression, add fractions, square a binomial, or create a monomial denominator • Look for opportunities to use the fundamental identities. Note which functions are in the final expression you want. Sines and cosines pair up well, as do secants and tangents, and cosecants and cotangents • If the preceding guidelines do not help, try converting all terms to sines and cosines • ALWAYS TRY SOMETHING! • THERE CAN BE MORE THAN ONE WAY! (TRY TO BE EFFICIENT!)

  5. Verify Trigonometric Identities

  6. Combining Fractions Before Using Identities

  7. Verifying a Trigonometric Identity

  8. Converting to Sines and Cosines

  9. Rationalizing the Denominator: Using Conjugates

  10. Verifying Trigonometric Identities

  11. Working with Each Side Separately

  12. Homework • Page 365-367 2-10 even, 31-49 odd, 63

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