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# Review Sheet for MATH 111 at UA

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This 20 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Arizona taught by a professor in Fall. Since its upload, it has received 16 views.

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Date Created: 02/06/15

Math 111 Review Problems Multiple Choice Please note that NOTA none of the above 1 1 Find z to be the nearest E of a degree Ar m 1pm a 414 b 486 c 369 d 531 e NOTA 2 Find the length of side p Round to two places r m 42 a 409 cm b 439 cm c 560 cm d 349 cm e NOTA 3 Convert 600 degrees to radians a 7 b 7 c 7 d J e NOTA 4 Convert 43 radians to degrees Round to the nearest degree a 14 b 774 c 493 d 126 e NOTA 5 Find the period of y 4 cot 2x a n b c 2n d e NOTA 3 Z 6 Find the phase shift of the function y 4 sin2er 1391 a r b l c d r e 2n 7 The solutions of coszx 7 cos x 7 2 0 are Where k denotes an arbitrary integer 77 a 2km b 32kn c H2k d 139I2k1391 e km 7239 8 The exact value of csc is a 2 b g c l d 72 e 9 An angle measured in standard position has the point 4 5 on its terminal ray What is cos 9 i i 4 Eom MMQM mane 1 10 Simplify the expression 72 1 using fundamental identities The result is cos a a cot2 a b see2 a C 0 d tan2 a e NOTA 5602 x 1 11 Lanx a 1 b tanx c tan3 x d cotx e cot2 x 12 Given that cos 6 and 9 is acute What is value of 9 a 30 b 45 c 60 d 15 e 430 13 Convert 21 radians to degrees Round to three significant figures a 00367 b 378 c 120 d 240 e NOTA 14 If the radius of a circle is 3 cm then the measure of the central angle that cuts an arc of length 6cm is 1 a 2rad b 120 c grad d 30 e 211 15 The length of an arc intercepted by an angle of 60 on a circle of radius 6 is a 1391 b 211 c 2 d E e E 16 Given that tan 6 and 9 is acute What is value of 9 a 30 b 45 c 60 d 15 e 430 17 The amplitude of function shown below is 15 u 13 in223 3723 71u a 7 b 1 c w d 7 e NOTA a y 23 cos2x2 b y 1 2 cosm7r c y 1 25inm 77r d y 2 3sin2x 72 e NOTA 19 The graph shows 3SinBXC B 20 Find me equaLion of the graph 1 x l x x r 1 x x x r 2uq 14 quot4 a y tan NW 6 b y tan 4x 0 y tan 2 d ytanx 114 e NOTA 21 Given the figure find x 94 9f 10 a 12 b 40 c 20 d 48 e 36 22 A central angle of 63 is in a circle of radius 18cm How long is the arc cut by the angle Round to 2 places a 1979 cm b 990 cm c 3958 cm d 7916 cm e NOTA 23 A pole casts a 10 foot shadow A man who is 6 feet tall casts a 35 foot shadow How tall is the pole a 583 ft b 210 ft c 1714 ft d 2100 ft e NOTA 24 Tim is 4 3 tall and his brother Tom is 5 9 If Tim casts a 9 foot shadow how long of a shadow will Tom cast a 665 ft b 1218 ft c 27m d 2444 ft e NOTA 25 A central angle of 70 degrees cuts an arc of 6 feet Find the radius of the circle a 6ft b 514 ft c 982 ft d 12ft e NOTA 26 A central angle cuts an arc of 45 In in a circle Whose radius is 9 In Find the measure of the angle Round to one place a 4050 b 4524 c 2865 d 2025 e NOTA Use the following figure for 27 and 28 I f m ill 739 27 Which ratio is equal to sec R 5 b L E d E NOTA a t m c t r e 28 Which ratio is equal to sin M E b E 5 d i NOTA a r t c t m e For 29 30 use 314 for 1391 Which of the listed values is NOT coterminal With the given value of x 29 x419 a 1465 b 71675 c 1779 d 2093 e NOTA 30 x 8605 a 6093 b 4837 c 3267 d 1697 e NOTA 3 For 31 and 32 A is in Quadrant Ill and sin A 5 31 Find cos A 1 b 5 2 a 5 5 C 5 32 Find tan A i b 2 3 a 4 4 C 3 3 d 5 e NOTA 4 d E e NOTA l l l l l l 3 33 Angle B is in standard position in Quadrant II and sin B Find a point on the terminal side of angle B a 3 58 b 37 c 773 d 73 e NOTA 34 Angle C is in standard position in quadrant Ill and cos C Find a point on the terminal side of angle C a Rs b J59 771 35 Find s1n exactly 6 J3 43 a 7 b T C E 7t 36 Find cos exactly J3 43 i a 7 b T C 2 c Es d J979 e NOTA d i e NOTA d e NOTA MH 37 Find z exactly n 60 9J5 18 a 9 b 7 c E d 18 e NOTA 38 A function y fx is periodic With period 6 If f2 3 find another value for x such that fx 3 a 3 b 5 c 8 d 9 e NOTA 77 39 Let m sin x With 71 S m S 1 lfx n With 0 S n S 3 is one solution find another solution a in b213917n c13917n d139In e NOTA For 40 41 42 and 43 consider the function y 75 7 4 sin3x 7 2 40 The amplitude is a 75 b 4 c 3 d 2 e NOTA 41 What is the vertical shift a 5 down b 5 up c 4down d 4up e NOTA 42 What is the period a 2n b 6n c 7 d n e NOTA 43 What is the horizontal shift 2 a 2left b 15 right c 2right d 3 left e NOTA 44 If cos m n and sin m k then a cos m n and sin m k b cos m n and sin m k c cos m n and sin m k d cos m n and sin m k e NOTA 45 A cosine function has period 12 and amplitude 8 It is also known that f5 30 is the maximum function value Find f1 1 a Not enough information b 24 c 22 d 14 e NOTA 7 J 46 Find exactly Sin 1 T 47 Find exactly cos 1 5 a6 6 03 3e 48 In AABC A 400 a 26m B 600 Find b a 35m b 39m c 19m 49 In AABC a5 b 3 ft C 68quot Find 0 Round to two places a 4524 ft b 227 ft c 673 ft 50 Solve sinx 5 on 0 2H 77 a E is the only solution e NOTA 51 What is the range of y sin x a 1 1 b 0211 c 1111 52 What is the range of y sin 1 x d 27m e NOTA d 477 ft e NOTA 7 b g is the only solution d mpg e NOTA 7Z39 77quot a 0211 b 11 c 0 H d e NOTA 53 What is the range of y tan 1 x 717 72 a oooo b 0 211 c 0 H d 7 a E e NOTA 54 y gx is periodic With period 5 g61 97 Find g211 a 5 b 61 c 97 d 247 e NOTA 55 A cosine function has period 12 and its maximum value at x 5 At What x value Will the function have a minimum a 8 b 11 c 14 d 17 e NOTA 56 A tangent function has period 16 a horizontal intercept at x 9 and no vertical shift At What x value Will the graph of this function have a vertical asymptote a 13 b 17 c 21 d 25 e NOTA Math 111 Review Problems Partial Credit Problems 1 Sketch angles in standard position a 300 degrees b 500 degrees c 150 degrees d 3n 2 Find x and y On Pm 3 Find 9 and x 1nr m 15 cm V 4 Find x and x 1 rm 20 cm V 5 Use the fundamental identities to find the exact value of sin x csc x and tan x given that 2 cosx 2 and cscxlt0 6 Use a sketch of the unit circle to explain Why a the function y sin x is periodic b the function y tan x has the vertical asymptotes Where it does c the function y cos x has the range that it does 7 Use the identity for cosx y to derive an identity for cos2x 7t 8 Find the exact value of SIHE 577 9 Find the exact value of COS E For Problems 10 11 and 12 find one solution analytically then find other solutions by any method 10 44 32 cos12x 51 on the interval 0 10 11 27 tan2x 65 on 0 50 12 500 25 sin52x 512 on 0 12 27139 13 Angle A 7 and angle A is in standard position The terminal side of angle A intersects the unit circle at the point a b Find the exact values of a and b 77 14 Repeat for angle B 57 15 Repeat for angle C T 16 Find a possible formula for each graph 17 Simplify each expression by Writing it Without using any trigonometric functions Find an exact value Whenever possible a sin 1sin 6 b sinsin 15 c sincosquot0 d sincosquotc e mnsin 1x 18 Find a possible formula for each dam mble a b 19 A sine function y fx has a period of 8 and amplitude of 3 It is also known that 7F 0 7139 2n Undefine 0 Undefine 0 d d 1 05 0 05 1 15 10 7 10 13 10 7 f 2 18 is a minimum value of the function a b C d 20 Solve each triangle ABC if possible If there is no such triangle explain how you know If two triangles are possible solve both a a5cmb6cmc7cm Find the maximum value of the function List three values for x that produce a maximum value List three values for x that product the average value of the function Write an equation for this function h a 617 in b 1152 in c 1741 in c a5ftb7ftC 78deg d a10m b6mB 25deg e a5cm b6cmB 35deg f A40degB50degc6ft 21 a On the given axes make a sketch ofy cosxa b Indicate on the graph approximate solutions to cos 7 4 c For each solution indicate the conesponding quadxant of the unit circle 22 Repeat 21 with y sink and sin x 23 A cosine mction y 806 has its average value at X 2 and X 10 a List three values that could be the period of this function b What is the largest possible period for this mction Explain

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