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Verifying Trigonometric Identities

Verifying Trigonometric Identities . Section 5.2 Math 1113 Created & Presented by Laura Ralston . Verifying Trigonometric Identities . In this section, we will study techniques for verifying trigonometric identities.

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Verifying Trigonometric Identities

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  1. Verifying Trigonometric Identities Section 5.2 Math 1113 Created & Presented by Laura Ralston

  2. Verifying Trigonometric Identities • In this section, we will study techniques for verifying trigonometric identities. • The key to verifying identities is the ability to use the fundamental identities and rules of algebra to rewrite trigonometric expressions

  3. Algebraic Expression: a collection of numbers, variables, symbols for operations, and grouping symbols; contains no equal sign 2(4x -3) – 6 2sin(4x – p) + 3 Equation: a statement that two mathematical expressions are equal. x + 2 = 5 sin x = 0 Review

  4. Contradiction: no values of the variable make the equation true x + 2 = x sin x = 5 Conditional: only 1 or several values of the variable make the equation true x + 2 = 5 ---- x = 3 sin x = 0 ----- x = 0 Three Categories of Equations

  5. Identity: equation is true for EVERY value of the variable x + x = 2x cos2x + sin2x = 1 2x = 2x

  6. Verifying an Identity is quite different from solving an equation. • There is no well-defined set of rules to follow in verifying trigonometric identities and the process is best learned by practice!!!

  7. Guidelines for Verifying Trig Identities • Work with one side of the identity at a time. It is often better to work with the more complicated side first. • Look for opportunities to factor an expression, add fractions, square a binomial, or create a monomial denominator.

  8. Look for opportunities to use the fundamental identities. Note which functions are in the final expression you want. • Sines and cosines pair up well, as do secants and tangents, and cosecants and cotangents.

  9. If all else fails, try converting all terms to sines and cosines. • Always try something!! Even paths that lead to dead ends give you insights.

  10. There can be more than one way to verify an identity. Your method may differ from that used by your instructor or classmates. • This is a good chance to be creative and establish your own style, but try to be as efficient as possible.

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