1 8.3 Trigonometric Identities In this section, we will study the following topics: o Using trig identities and algebra to simplify trigonometric expressions o Verifying trigonometric identities

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3 Use the fundamental trig identities to simplify the following trigonometric expressions. Simplifying Trig Expressions

4 Use the fundamental trig identities to simplify the following trigonometric expressions.

5 Simplifying Trig Expressions Use the fundamental trig identities to simplify the following trigonometric expressions.

6 Simplifying Trig Expressions Use the fundamental trig identities to simplify the following trigonometric expression.

7 Verifying Trig Identities Algebraically Goal: Get one side of the equation equal to the other! Strategy: Hold one side of the equation constant Transform one side of the equation into the other using the trig identities. Look for: Reciprocal identities Quotient identities Pythagorean identities Even/Odd Identities When you have successfully verified the identity, write Q.E.D. at the end. Quod erat demonstrandum = “Which was to be proven”

8 Verifying Trig Identities Algebraically HELPFUL HINTS: 1. Only work with ONE SIDE OF THE EQUATION AT A TIME. Do not use inverse operations! (i.e. do not ‘move’, multiply, or divide terms from both sides of the equation.) 2. You usually try to SIMPLIFY THE MORE COMPLICATED SIDE. Leave the other side alone. 3. When other options are not available, you can CHANGE ALL TERMS INTO EXPRESSIONS CONTAINING SINE AND /OR COSINE. Then simplify.

9 Verify the trigonometric identity: Verifying Trig Identities Algebraically

10 Verify the identity: Verifying Trig Identities Algebraically

11 Verify the identity: Verifying Trig Identities Algebraically

12 Verify the identity: Verifying Trig Identities Algebraically

13 Verify the identity: Verifying Trig Identities Algebraically

14 Verify the identity: Verifying Trig Identities Algebraically

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