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8.3 Trigonometric Identities

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

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8.3 Trigonometric Identities

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

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

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

  4. Simplifying Trig Expressions 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 expression.

  6. 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” 

  7. Verifying Trig Identities Algebraically • HELPFUL HINTS: • 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.) • You usually try to SIMPLIFY THE MORE COMPLICATED SIDE. Leave the other side alone. • When other options are not available, you can CHANGE ALL TERMS INTO EXPRESSIONS CONTAINING SINE AND /OR COSINE. Then simplify.

  8. Verifying Trig Identities Algebraically Verify the trigonometric identity:

  9. Verifying Trig Identities Algebraically Verify the identity:

  10. Verifying Trig Identities Algebraically Verify the identity:

  11. Verifying Trig Identities Algebraically Verify the identity:

  12. Verifying Trig Identities Algebraically Verify the identity:

  13. Verifying Trig Identities Algebraically Verify the identity:

  14. End of Section 8.3

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