1. Verifying Trigonometric Identities
Digital Lesson
Verifying Trigonometric Identities

2. Guidelines for Verifying Identities
1. Start with the most complicated side of the equation.
2. Factor an expression, add fractions, square a binomial, or create s monomial denominator, if possible.
3. Use the fundamental identities, whenever possible.
4. Convert all terms to sines and cosines.
5. Always try something.
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Guidelines for Verifying Identities

3. Example: Verify Identity
Verify the identity
Start with the more complicated side.
Pythagorean Identity
Simplify.
Reciprocal Identity
Quotient Identity
Simplify.
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Example: Verify Identity

4. Graphing Utility: Verify Identity
Verify the identity
Identical Values
Table:
Identical Graphs
–2 2
–0.5
1.5
–2 2
–0.5
1.5
Graph:
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Graphing Utility: Verify Identity

5. Example: Verify Identity
Verify the identity
Pythagorean Identity
Reciprocal Identity
Rule of Exponents
Quotient Identity
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Example: Verify Identity

6. Sum and Difference Formulas
Signs are the same
Example:
Verify the identity
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Sum and Difference Formulas

7. Sum and Difference Formulas (continued)
Signs are opposite
Signs are the same
Signs are the same
Opposite signs
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Sum and Difference Formulas (continued)

8. Double-Angle Formulas
Example:
Verify the identity
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Double-Angle Formulas

9. Double-Angle Formulas (continued)
Example:
Verify the identity
Sum Formula
Double-Angle Formula
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Double-Angle Formulas (continued)

10. Half-Angle Formulas: Example:
Use the half-angle formula to find the exact value of sin 22.5°.
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Half-Angle Formulas