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**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

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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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**Example: If and Ө is in quadrant II, find each function value. (Cont.)**

b) sin Ө c) cot (- Ө ) 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 2a2 – 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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Copyright © Cengage Learning. All rights reserved. 5.1 Using Fundamental Identities.

Copyright © Cengage Learning. All rights reserved. 5.1 Using Fundamental Identities.

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