Class: _ Date: _ Ch. 4 - Trigonometry Quiz Review 1. Find the quadrant in which the given angle lies. 154 a. Quadrant I b. Quadrant II c. Quadrant III d. Quadrant IV e. None of the above 2. Find the supplement of the following angle. 113 a. Supplement: 68 b. Supplement: 247 c. Supplement: 67 d. Supplement: 23 e. Supplement: 113 3. The point Ê Ë Á8,15ˆ is on the terminal side of an angle in standard position. Determine the exact value of tanq. a. tanq = 15 8 b. tanq = 15 17 c. tanq = - 8 15 d. tanq = 17 15 e. tanq = - 17 15 1
4. Evaluate the trigonometric function using its period as an aid. sin p a. sin p = b. sin p = 1 c. sin p = 4 d. sin p = 0 e. sin p = 4 5. Find angle 60 in radian measure as a multiple of p. 4p a. 3 p 2 b. 2 2 c. p p d. 3 e. 3p 6. Find (if possible) the complement of the following angle. p 9 a. Complement: 7p 9 b. Complement: p c. Complement: - p 9 d. Complement: 7p 18 e. Complement: 9 7p 2
7. Find the values of q in degrees ( 0 < q < 90 ) and radians ( 0 < q < p / 2) without the aid of a calculator. sin q = 0 a. q = 30 = p 6 b. q = 90 = p 2 c. q = 60 = p 3 d. q = 0 = 0 e. q = 45 = p 4 8. Convert 92.674 to D M'S" form. a. 92 30'20" b. 92 33'22" c. 92 20'13" d. 92 40'26" e. 92 10'7" 3
9. Find the reference angle q, and select q and q in standard position. q = 156 a. q = -34 d. q = -24 b. q = 39 e. q = 24 c. q = 34 4
10. Determine two coterminal angles (one positive and one negative) for q = 5p 6. a. b. c. d. e. 11p 13p,- 6 6 13p 7p,- 6 12 17p 6,- 7p 6 5p 7p,- 3 18 19p 17p,- 6 6 11. Find the exact values of the three trignometric functions of the angle q (sinq, cosq, tanq) shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.) a = 9, b = 40 a. sin q = 40 41, cosq = 9 41, tanq = 9 40 b. sin q = 9 40, cosq = 41 41, tanq = 9 40 c. sin q = 41 40, cosq = 9 41, tanq = 40 9 d. sin q = 40 41, cosq = 9 41, tanq = 40 9 e. sin q = 41 41, cosq = 9 40, tanq = 9 40 5
12. Find the complement of the following angle. 29 a. Complement: 212 b. Complement: 29 c. Complement: 62 d. Complement: 151 e. Complement: 61 13. Find the values of q in degrees ( 0 < q < 90 ) and radians ( 0 < q < p / 2) without the aid of a calculator. csc q = 1 a. q = 90 = p 2 b. q =0 = 0 c. q = 60 = p 3 d. q = 30 = p 6 e. q =45 = p 4 6
14. Use the Pythagorean Theorem to determine the third side and then find the three trignometric functions of q: sin q, cot q, and csc q cos q = 24 25 a. sin q = 24 25, cot q = 24 7, cscq = 25 24 b. sin q = 7 25, cot q = 7 24, cscq = 25 7 c. sin q = 7 24, cot q = 24 25, cscq = 24 7 d. sin q = 7 25, cot q = 24 7, cscq = 25 7 e. sin q = 25 7, cot q = 24 7, cscq = 7 25 15. A guy wire runs from the ground to a cell tower. The wire is attached to the cell tower a = 160 feet above the ground. The angle formed between the wire and the ground is q = 35 (see figure). How long is the guy wire? Round your answer to one decimal place. a. The guy wire is about 93.0 feet long. b. The guy wire is about 279.0 feet long. c. The guy wire is about 836.9 feet long. d. The guy wire is about 139.5 feet long. e. The guy wire is about 557.9 feet long. 7
16. State the quadrant in which q lies if cosq < 0 and tanq < 0. a. Quadrant II b. Quadrant III c. Quadrant I d. Quadrant IV 17. Find the values of q in degrees ( 0 < q < 90 ) and radians ( 0 < q < p / 2) without the aid of a calculator. sec q = 2 a. q = 90 = p 2 b. q =0 = 0 c. q = 30 = p 6 d. q = 60 = p 3 e. q = 45 = p 4 18. Find (if possible) the supplement of the following angle. p 12 a. Supplement: p 12 b. Supplement: 12 11p c. Supplement: p d. Supplement: 11p 12 e. Supplement: - p 12 8
19. Use the Pythagorean Theorem to determine the third side and then find the three trignometric functions of q: sin q, cot q, and csc q tan q = 12 5 a. sin q = 5 13, cot q = 5 12, cscq = 13 5 b. sin q = 12 13, cot q = 5 12 c. sin q = 13 12, cot q = 5 12 d. sin q = 12 13, cot q = 12 5 13, cscq = 12 12, cscq = 13 13, cscq = 12 e. sin q = 12 5, cot q = 5 13, cscq = 5 12 20. The point Ê Ë Á-7,- 24ˆ is on the terminal side of an angle in standard position. Determine the exact value of tanq. a. tanq = - 25 24 b. tanq = 31 24 c. tanq = - 24 25 d. tanq = 24 7 e. tanq = - 1 24 21. Determine two coterminal angles (one positive and one negative) for q = -462. a. 258,- 282 b. 258,- 102 c. 168,- 282 d. 348,- 372 e. 168,- 192 9
22. Solve for x as indicated. a = 38 a. x = 38 3 b. x = 40 2 c. x = 40 3 d. x =38 2 e. x = 39 3 23. Given the figure below, determine the value of sin q. a. sin q = 5 12 b. sin q = 12 5 c. sin q = - 5 13 d. sin q = 12 13 e. sin q = - 5 12 10
24. Evaluate the trigonometric function using its period as an aid. cos 7p 3 a. cos 7p 3 = 1 2 b. cos 7p 3 = 2 c. cos 7p 3 = d. cos 7p 3 = 2 e. cos 7p 3 = 1 2 11
Ch. 4 - Trigonometry Quiz Review Answer Section 1. ANS: B PTS: 1 REF: 4.1.41a 2. ANS: C PTS: 1 REF: 4.1.54b 3. ANS: A PTS: 1 REF: 4.4.13 OBJ: Determine value of trig function given point on terminal side 4. ANS: D PTS: 1 REF: 4.2.35 5. ANS: D PTS: 1 REF: 4.1.57a 6. ANS: D PTS: 1 REF: 4.1.31a 7. ANS: D PTS: 1 REF: 4.3.57a 8. ANS: D PTS: 1 REF: 4.1.83b OBJ: Convert decimal degree to DMS form 9. ANS: E PTS: 1 REF: 4.4.45 10. ANS: C PTS: 1 REF: 4.1.29a OBJ: Determine two coterminal angles (radians) 11. ANS: B PTS: 1 REF: 4.3.5 12. ANS: E PTS: 1 REF: 4.1.53a 13. ANS: A PTS: 1 REF: 4.3.57b 14. ANS: D PTS: 1 REF: 4.3.14 15. ANS: B PTS: 1 REF: 4.3.71a 16. ANS: A PTS: 1 REF: 4.4.19 OBJ: Determine quadrant given constraints 17. ANS: D PTS: 1 REF: 4.3.59a 18. ANS: D PTS: 1 REF: 4.1.32a 19. ANS: B PTS: 1 REF: 4.3.16 20. ANS: D PTS: 1 REF: 4.4.15 OBJ: Determine value of trig function given point on terminal side 21. ANS: B PTS: 1 REF: 4.1.51b OBJ: Determine two coterminal angles (degrees) 22. ANS: A PTS: 1 REF: 4.3.64 23. ANS: D PTS: 1 REF: 4.4.10b OBJ: Determine trig value from diagram 24. ANS: E PTS: 1 REF: 4.2.37 1