MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Transcription

1 MATH 1113 Exam III PRACTICE TEST FALL 2015 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. 1) 1) B 27 A 120 C Find cos B and cot B. A) cos B = 9 9 -; cot B = C) cos B = --; 40 cot B = B) cosb= - -;cotb = D) cos B=- 5-; cot B 40 = - Find the requested function value of 0. 2) If sin 0 =, cos 6 =, and tan 0 =, then find csc 6, sec 6, and cot 0. 2) 8'.j 8 A) csc 6 ; sec 6 = --; cot = 5 = 39 C) csc 0 = --; sec 6 = ; cot 6 = B) csc ti , sec 0=-; cot 0= D) csc 0 = ---; sec 6 = --; cot 0 = Find the sign of the six trigonometric function values for the given angle. 3)288-3) A) Positive: cosine, secant; negative: sine, tangent, cotangent cosecant B) Positive: all C) Positive: sine, tangent, cotangent cosecant; negative: cosine and secant D) Positive: sine and cosecant; negative: cosine, tangent, cotangent, secant 1

2 Find. F 4) tan lsin -i I 8 1 4) yj. A 64 B 8 C 8 D y Find the exact value. 5) Given that cos 0 = -15 with 0 in quadrant I, find sin 20. 5) 17 A 24 B 161 C 16 D Simplify. 6) sin4 x - cos4 x 6) A) Cos 2x B)- Cos 2x C) sin 2x D) Cos x 7)2_csCx CSC 2 x A) 2 cos2 x -1 B) 2 sin2 x -1 C) 2 (sin2 x -1) D) 2 cos 2x 7) Find the trigonometric function value of angle 0. 8)cot0=--- and 0iri quadrant II 8) Find csc 0. 3,T13 3,113 A) B) - C) D) Find the exact trigonometric function value. 9) tan 690 9) B)1 C) -'J D)4 Find the reference angle for the given angle. 10) ) A) -45 B) 30 C) 450 D) 900 Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. 11)244' 11) A) 5140; -26 B) 424 ; -116 C) 604 ; -116 D) 604 ;

3 Without using a calculator, give the exact trigonometric function values with rational denominators. 12) sin ) A) \F3 B)$ C) - - D)4 13) cot ) A) F2 B)+ D)1 14) sec 30 14) A)2 B)1 C) ^\/2

4 Solve the problem. 15) The path between three landmarks in a national park form a right triangle. The oldest living 15) evergreen tree is at point A, the ranger station is at point B, and the natural hotspring is at point C. The right angle is at point C, and there is a 600 angle at point B. If the distance between the hotspring and the evergreen tree is 523 yards, find the distance, x, from the hotspring to the ranger station. DE Ho 60 A /523 yd C A) yd B) yd C) yd D) yd Convert to decimal degree notation. Round to two decimal places. 16) ) A) B) C) D) Find the exact acute angle 0 for the given function value. 17) tan 0=1-17) A) 45 B) 30 C) 60

5 Solve. 18) A bicyclist's average linear speed during a race was 37 mph. His bicycle wheel has a 17-in. 18) diameter. What was the angular speed of the wheel in revolutions per hour? Round to the nearest tenth. [1 Mile =63360 inches] A) 137,901.2 revolutions per hour B) revolutions per hour C) 43,895.3 revolutions per hour D) 2.2 revolutions per hour 19) A bicycle wheel rotates 44 times in 1 minute. Through how many degrees does a point on the tip of 19) the wheel move in 15 seconds? A) 660 B) 3960 C) 264 D) 900 Convert to degree measure. Round to two decimal places, if necessary. 20) A) B) 315 C) D) n

6 Solve. 21) A blimp is 1900 meters high in the air and measures the angles of depression to two stadiums to the 21) west of the blimp. If those measurements are 84.7 and 17.70, how far apart are the two stadiums to the nearest meter? A) 18,575 m B) 4341m C) 5777 m D) 6130 m Find the amplitude, period or phase shift. 22) Find the amplitude of y = 2 sin [3x 22) +.J. A)6 B) - - C)3 D)2 23) Find the period of y = 2cos [3x + ]. A) - - B)1 C)2 D)t 23)

7 Match the function with its graph. TC 71 24)1)y=sin x--- 2)y=cos x+-- 24) 3)y=sin x+ -- 4)y=cos x_-- 11) A) C) D) A) 1B, 2D, 3C, 4A B) 1A, 2B, 3C, 4D C) 1C, 2A, 3B, 4D D) 1A, 2D, 3C, 4B

8 Multiply and simplify. 25) sin U (sec U tan U + csc U + cot U) A)1+2sin2 U B)sin2 U-1+ cos U C) sin U+2 sec U D)sec2 U+ cos U 25) 26) (cos x - sin x)2 A)cos2x+2 sin x-sin2x B)1 C) 1-2 sin x cos x D) cos2x+2sin2x 26) Simplify. 27) Rationalize the numerator. tan 3 cos A) -TC cos i + cos p B) 1 cos 3 - C) sin D) 1 + sin (3 sin p 1 + cos p cos p 27) Find the exact value by using a half-angle identity. 28) cos 750 A)2+ B)-2- C)-2+ D)2-29) sin-s- NJ A)fJ2J B)+j2- C)+ J2 +J D)f J2 +J 1.1

9 Find the exact value. 30) Given that sin 0 = - with 0 in quadrant IV, find cos ) A )-24 B 24 C D 7 25 ) 25 )- 25 ) 25 Simplify. 31) sin4 x - cos4 x A)- cos 2x B) cos 2x C) Cos x D) sin 2x 31) 32 3csc2x 32) A) 3 (sin2 x -1) B) 3 cos 2x C) 3 cos2 x -1 D) 3 sin2 x -1