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Published byGavin Fitzpatrick Modified over 2 years ago

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Using Fundamental Identities Objectives: 1.Recognize and write the fundamental trigonometric identities 2.Use the fundamental trigonometric identities to evaluate trigonometric functions, simplify trigonometric expressions, and rewrite trigonometric expressions

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WHY??? Fundamental trigonometric identities can be used to simplify trigonometric expressions, such as for the coefficient of friction.

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Fundamental Trigonometric Identities Reciprocal Identities Quotient Identities

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Fundamental Trigonometric Identities Pythagorean Identities Even/Odd Identities

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Fundamental Trigonometric Identities Cofunction Identities

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Example: If and Ө is in quadrant II, find each function value. a) sec Ө To find the value of this function, look for an identity that relates tangent and secant. Tip: Use Pythagorean Identities.

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b) sin Ө 7 c) cot ( Ө ) Example: If and Ө is in quadrant II, find each function value. (Cont.) Tip: Use Quotient Identities. Tip: Use Reciprocal and Negative-Angle Identities.

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2. Use the values cos x > 0 and identities to find the values of all six trigonometric functions. What quadrant will you use? 1st quadrant

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Using Identities to Evaluate a Function Use the given values to evaluate the remaining trigonometric functions (You can also draw a right triangle)

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

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Example: Simplify 1.Factor csc x out of the expression.

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

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3.Use Reciprocal identities to simplify the expression.

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Simplifying a Trigonometric Expression

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Factoring Trigonometric Expressions -Factor the same way you would factor any quadratic. - If it helps replace the trig word with x -Factor the same way you would factor

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Make it an easier problem. Let a = csc x 2a 2 – 7a + 6 (2a – 3)(a – 2) Now substitute csc x for a.

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1.Use Pythagorean identities to get one trigonometric function in the expression.

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2.Now factor.

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Factoring Trigonometric Expressions

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More Factoring

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Adding Trigonometric Expressions (Common Denominator)

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Adding Trigonometric Expressions

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Rewriting a Trigonometric Expression so it is not in Fractional Form

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Trigonometric Substitution

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