Simple Trig Identities

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Presentation transcript:

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 Since we know that x = cos t and y = sin t …

Reciprocal Identities Identities given by definition

Pythagorean Identities Consider that x2 + y2 = 1 Thus Similarly

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

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

Experiment with what your calculator does with these expressions Practice Try these Experiment with what your calculator does with these expressions

Assignment Lesson 2.4b Page 167 Exercises 55 – 97 odd