Trigonometric Identity Practice
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1 Trigonometric Identity Practice Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Identify the expression that completes the equation so that it is an identity. = Simplify the trigonometric expression. 2. a. tanq b. 1 c. cotq d. sinq 3. Solve the equation for 0 < 2p. Write your answer as a multiple of p, if possible. 4. 4cosq + 1 = 2cosq The equation models the height h in centimeters after t seconds of a set of keys attached to the end of a spring that has been stretched and then released. When will the set of keys first be 3 inches above the resting position? a. 1.6 seconds b. 1 second c. 3.3 seconds d. 2 seconds
2 9. Find the complete solution of the equation in radians. a. b. c. d. Find the exact value of the expression. 10. cos 255 Find the value of the trigonometric expression. 11. sin 50 cos 170 cos 50 sin cos 150 cos 120 sin 150 sin 120 a. b. 0 c. 1 d What is the simplified form of sin(x + p)? a. cos x b. sin x c. sin x d. cos x Rewrite the expression as a trigonometric function of a single angle measure. 14. Short Answer Verify the identity. Justify each step The equation models the height h in centimeters after t seconds of a weight attached to the end of a spring that has been stretched and then released.
3 a. Solve the equation for t. b. Find the times at which the weight is first at a height of 1 cm, of 3 cm, and of 5 cm above the rest position. Round your answers to the nearest hundredth. c. Find the times at which the weight is at a height of 1 cm, of 3 cm, and of 5 cm below the rest position for the second time. Round your answers to the nearest hundredth. 18. Use an angle sum identity to verify the identity.
4 Trigonometric Identity Practice Answer Section MULTIPLE CHOICE 1. ANS: A PTS: 1 DIF: L2 REF: 14-1 Trigonometric Identities TOP: 14-1 Example 2 KEY: trigonometric identities 2. ANS: B PTS: 1 DIF: L1 REF: 14-1 Trigonometric Identities TOP: 14-1 Example 3 KEY: trigonometric identities simplifying trigonometric expressions 3. ANS: B PTS: 1 DIF: L2 REF: 14-1 Trigonometric Identities TOP: 14-1 Example 3 KEY: trigonometric identities simplifying trigonometric expressions 4. ANS: A PTS: 1 DIF: L1 TOP: 14-2 Example 5 KEY: trigonometric equation radian measure 5. ANS: B PTS: 1 DIF: L1 TOP: 14-2 Example 6 KEY: trigonometric equation radian measure
5 6. ANS: D PTS: 1 DIF: L2 TOP: 14-2 Example 6 KEY: radian measure tangent function inverse of a trigonometric equation 7. ANS: B PTS: 1 DIF: L2 REF: 14-6 Angle Identities OBJ: Angle Identities TOP: 14-6 Example 2 KEY: angle identities cofunction identity cosine function sine function 8. ANS: D PTS: 1 DIF: L1 TOP: 14-2 Example 7 KEY: cosine function problem solving radian measure 9. ANS: D PTS: 1 DIF: L3 TOP: 14-2 Example 6 KEY: radian measure cosine function sine function inverse of a trigonometric equation 10. ANS: A PTS: 1 DIF: L1 REF: 14-6 Angle Identities TOP: 14-6 Example 4 KEY: angle identities angle difference identities angle sum identities exact values of trigonometric functions
6 11. ANS: D PTS: 1 DIF: L2 REF: 14-6 Angle Identities TOP: 14-6 Example 5 KEY: angle identities exact values of trigonometric functions angle difference identities 12. ANS: B PTS: 1 DIF: L2 REF: 14-6 Angle Identities TOP: 14-6 Example 5 KEY: angle identities exact values of trigonometric functions angle sum identities 13. ANS: C PTS: 1 DIF: L2 REF: 14-6 Angle Identities TOP: 14-6 Example 5 KEY: angle identities sine function 14. ANS: D PTS: 1 DIF: L2 REF: 14-6 Angle Identities TOP: 14-6 Example 4 KEY: angle identities angle difference identities SHORT ANSWER 15. ANS: tangent identity and cotangent identity
7 = Write the fractions with a common denominator. = Add. = Pythagorean identity PTS: 1 DIF: L1 REF: 14-1 Trigonometric Identities TOP: 14-1 Example 1 KEY: trigonometric identities Pythagorean Identities 16. ANS: Write the fractions with a common denominator. Distributive property Subtract. Cotangent identity Reciprocal identity Simplify.
8 Pythagorean identity Reciprocal identity PTS: 1 DIF: L3 REF: 14-1 Trigonometric Identities TOP: 14-1 Example 2 KEY: Pythagorean Identities Reciprocal Trigonometric Identities trigonometric identities 17. ANS: a. b s, 1.08 s, 0.74 s c s, 4.08 s, 3.74 s PTS: 1 DIF: L2 TOP: 14-2 Example 7 KEY: problem solving cosine function radian measure inverse of a trigonometric equation multi-part question 18. ANS: Write as angle sum. Angle sum identity Simplify. Pythagorean identity Distributive Property Simplify. PTS: 1 DIF: L1 REF: 14-7 Double-Angle and Half-Angle Identities OBJ: Double-Angle Identities
9 TOP: 14-7 Example 2 KEY: angle identities double-angle identities
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