Verifying Trigonometric Identities Digital Lesson Verifying Trigonometric Identities

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. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Guidelines for Verifying Identities

Example: Verify Identity Verify the identity Start with the more complicated side. Pythagorean Identity Simplify. Reciprocal Identity Quotient Identity Simplify. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Example: Verify Identity

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: Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Graphing Utility: Verify Identity

Example: Verify Identity Verify the identity Pythagorean Identity Reciprocal Identity Rule of Exponents Quotient Identity Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Example: Verify Identity

Sum and Difference Formulas Signs are the same Example: Verify the identity Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Sum and Difference Formulas

Sum and Difference Formulas (continued) Signs are opposite Signs are the same Signs are the same Opposite signs Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Sum and Difference Formulas (continued)

Double-Angle Formulas Example: Verify the identity Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Double-Angle Formulas

Double-Angle Formulas (continued) Example: Verify the identity Sum Formula Double-Angle Formula Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Double-Angle Formulas (continued)

Half-Angle Formulas: Example: Use the half-angle formula to find the exact value of sin 22.5°. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Half-Angle Formulas