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Using Fundamental Identities Objectives: 1.Recognize and write the fundamental trigonometric identities 2.Use the fundamental trigonometric identities.

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Presentation on theme: "Using Fundamental Identities Objectives: 1.Recognize and write the fundamental trigonometric identities 2.Use the fundamental trigonometric identities."— Presentation transcript:

1 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

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

3 Fundamental Trigonometric Identities Reciprocal Identities Quotient Identities

4 Fundamental Trigonometric Identities Pythagorean Identities Even/Odd Identities

5 Fundamental Trigonometric Identities Cofunction Identities

6 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.

7 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.

8 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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12 Using Identities to Evaluate a Function Use the given values to evaluate the remaining trigonometric functions (You can also draw a right triangle)

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

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

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

16 3.Use Reciprocal identities to simplify the expression.

17 Simplifying a Trigonometric Expression

18 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

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

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

21 2.Now factor.

22 Factoring Trigonometric Expressions

23 More Factoring

24 Adding Trigonometric Expressions (Common Denominator)

25 Adding Trigonometric Expressions

26 Rewriting a Trigonometric Expression so it is not in Fractional Form

27 Trigonometric Substitution


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