Using Fundamental Identities

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Using Fundamental Identities

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Presentation transcript:

Using Fundamental Identities Objectives: Recognize and write the fundamental trigonometric identities Use the fundamental trigonometric identities to evaluate trigonometric functions, simplify trigonometric expressions, and rewrite trigonometric expressions

Fundamental Identities

Fundamental Trigonometric Identities Pythagorean Identities

Simplify an Expression Simplify cot x cos x + sin x. Click for answer.

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2. Use Pythagorean identities to simplify the expression in the parentheses.

3. Use Reciprocal identities to simplify the expression.

Simplifying a Trigonometric Expression

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c) tan x sin x + cos x = sec x Proving an Identity Prove the following: a) sec x(1 + cos x) = 1 + sec x = sec x + sec x cos x = sec x + 1 1 + sec x L.S. = R.S. b) sec x = tan x csc x c) tan x sin x + cos x = sec x L.S. = R.S. L.S. = R.S. 5.4.8

= (sin2x - cos2x)(sin2x + cos2x) = (1 - cos2x - cos2x) = 1 - 2cos2x Proving an Identity d) sin4x - cos4x = 1 - 2cos2 x = (sin2x - cos2x)(sin2x + cos2x) = (1 - cos2x - cos2x) = 1 - 2cos2x 1 - 2cos2x L.S. = R.S. e) L.S. = R.S. 5.4.9

Proving an Identity f) L.S. = R.S. 5.4.10