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Math Analysis Day III. Verifying Trigonometric Identities (5.2) 1/17/12 A dog is the greatest gift a parent can give a child. OK, a good education, then a dog. John Grogan, born March 20, 1957, American journalist and non-fiction writer You can use trigonometric identities to simplify an expression for a rate of change. I. Introduction Match the following words with the example and with the working method. Expression 3x – 6 = 0 verify Conditional Equation 3x – 6 = 3(x – 2) simplify Identity 3x – 6 solve What is the difference between an identity and a conditional equation? Guidelines for Verifying Trigonometric Identities Work with ______________side of the equation at a time - the more complicated side first. ______________ for factoring, adding fractions, squaring binomials, or creating monomial denominators. Look for fundamental ________________________. If nothing works, try_________________________ to sines and cosines. ______________________ try something!!! II. Verifying Trigonometric Identities Example 1. Verifying a Trigonometric Identity Verify: tan2 = Your Turn: = csc2 Example 2. Combining Fractions Before Using Identities Verify: 2 tan2 = + Your Turn: + = 2 sec2 Example 3. Verifying a Trigonometric Identity Verify: sin2 x(csc x–1)(csc x+1) = 1 - sin2 x Your Turn: ( 1 – tan )2 = sec2 - 2 tan Example 4. Converting to Sines and Cosines Verify: + = sec2 csc Your Turn: sec – tan sin = cos Example 5. Verifying Trigonometric Identities Verify: - = 5(tan - sec ) Your Turn: = 1 + cos Example 6. Working with Each Side Separately Verify: = sec csc Your Turn: tan sin = sec - cos Example 7. Calculus Example csc4 x cot x = csc2 x(cot x + cot3 x) Your Turn: cot5 = cot3 csc2 - cot3