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Simple Trig Identities

Simple Trig Identities. Lesson 2.4b. Definition of An Identity. Any equation that is true for every number in the domain of the equation. Example 2x + 12 = 2(x + 6) Trig identities Ratio Identities Reciprocal identities Pythagorean identities. Ratio Identities.

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Simple Trig Identities

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  1. Simple Trig Identities Lesson 2.4b

  2. Definition of An Identity • Any equation that is true for every number in the domain of the equation. • Example • 2x + 12 = 2(x + 6) • Trig identities • Ratio Identities • Reciprocal identities • Pythagorean identities

  3. Ratio Identities • Since we know that x = cos t and y = sin t …

  4. Reciprocal Identities • Identities given by definition

  5. Pythagorean Identities • Consider that x2 + y2 = 1 • Thus • Similarly

  6. Working with Identities • Simplifying expressions using identities • Given • Simplify • Give a justification for each step

  7. Working with Identities • Tips • In an expression, look for a part of the expression that looks like part of one of the identities • Substitute that in • Look for factors to cancel • Look for terms of an expression that can be combined to form one of the identities • Also possible to look at identities in different forms

  8. Practice • Try these Experiment with what your calculator does with these expressions

  9. Assignment • Lesson 2.4b • Page 167 • Exercises 55 – 97 odd

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