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# Review Sheet for MATH 111 at UA

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This 18 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 21 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 Find 2 to be the nearest i ofa degree 10 4cm 3cm a 414 b 486 c 369 d 531 e NOTA 2 Find the length of side p Round to two places 6cm a 409 cm b 439 cm c 560 cm d 349 cm e NOTA 3 Convert 600 degrees to radians a 101 b amp c 261 d 3L e NOTA 3 9 9 9 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 ofy 4 cot 2x a TC b E c 271 d 1 e NOTA 2 4 6 Find the phase shift of the function y 4 sin2739x TE a l b l c 1 d l e 27 4 2 2 4 7 The solutions of coszx 7 cos x 7 2 0 are where k denotes an arbitrary integer a 21m b g2k7t cn2k commm ek7t 8 The exact value of csc is B 2 a 2 b Y c d 72 e 7 9 An angle measured in standard position has the point 45 on its terminal ray What is cos 6 b d e A 4 5 agt m E m s 10 Simplify the expression 1 using fundamental identities The result is cos a a cot2 a b sec2 at c 0 d tan2 a e NOTA 2 11 sec x l tanx a l b tanx c tan3x d cotx e cot2 x 3 12 Given that cos 639 Y and 6 is acute what is value of 6 a 300 b 450 c 60 d 150 e 730 13 Convert 21 radians to degrees Round to three significant gures a 00367 b 378 c 120 d 240 e NOTA 14 If the radius ofa circle is 3 cm then the measure of the central angle that cuts an arc of length 6cm is a Zrad b 120 c md d 30 e 21 15 The length of an arc intercepted by an angle of 60D on a circle of radius 6 is ll39 1 a 1 b 21 c 2 d 7 e 7 2 12 16 Given that tan 6 T and 6 is acute What is value of e a 30 b 45 c 60 d 15 e 730 17 The amplitude of inction shown below is 15 H 13 an225 H725 71u a 7 b 1 c 77 d 7 e NOTA 18 The equation ofthe graph below is a y23cos2x2 b y12cosDc7r c y125in7rxiir d y235in2x72 e NOTA 19 The graph showsy 3 sinBx C B a 1 b1 c W d i e i 20 Find the equation ofthe graph a ytanx b ytan4x 1 c ytan2x d ytan5x e NOTA 21 Given the figure find 24 20 10 a 12 b 40 c 20 d 48 e 36 22 A eential angle of 63 is in acircle ofmdius 18cm How long is the are cut by the angle Round to 2 places a 1979cin 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 583ft b 210ft c 1714ft d 2100ft e NOTA 24 Tim is 4 3 tall and his brother Tom is 5 9 If Tim casts a 9 foot shadow how long ofa shadow will Tom cast a 665ft b 1218ft c 271ft d 2444ft e NOTA 25 A central angle of 70 degrees cuts an arc of 6 feet Find the radius of the circle a 6ft b 514ft c 982ft d 12ft e NOTA 26 A central angle cuts an arc of 45 m in a circle whose radius is 9 In Find the measure of the angle Round to one place a 40500 b 45240 c 28650 d 2025o e NOTA Use the following figure for 27 and 28 R t m M T r 27 Which ratio is equal to sec R a 5 b L c E d E e NOTA t m t r 28 Which ratio is equal to sin M a E b E c 5 d i e NOTA r t t m For 29 30 use 3 14 for TE Which of the listed values is NOT coterminal with the given value of x 29 x 419 a 1465 b 71675 c 1779 d 2093 e NOTA 30 x 8605 a 6093 b 4837 c 3267 d 1697 e NOTA For 31 and 32 A is in Quadrant III and sinA 3 1 Find cos A 4 4 3 a 7 b 7 c 7 d 7 e NOTA 5 5 5 5 32 Find tan A 3 3 4 4 a 7 b 7 c 7 d 7 e NOTA 4 4 3 3 3 33 Angle B is in standard pos1tion 1n Quadrant II and Sin B 7 E Find a point on the terminal side of angle B a 3 b 37 c 773 d 73 e NOTA 34 Angle C is in standard position in quadrant III and cos C Find a point on the terminal side of angle C a J59 b 459 c My d My e NOTA 35 Find sin exactly J5 J3 1 a 7 b 7 c 7 d 7 e NOTA 2 2 2 47239 36 Find cos exactly a b i c l d l e NOTA 2 2 2 2 37 Findzexactly Z 9 600 a 9 b i c E d 18 e NOTA 2 B 3 8 A function y x is periodic with period 6 If f2 3 nd another value for x such that fx 3 a 3 b 5 c 8 d 9 e NOTA 39 Let m sin x with 71 S m S l Ifx n with 0 S n S g is one solution nd another solution a in b 271771 c 71711 d7tn e NOTA For 40 41 42 and 43 consider the functiony 75 7 4 sin3x 7 2 40 The amplitude is a 75 b 74 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 271 b 671 c 2 d TE e NOTA 43 What is the horizontal shift a 2left b 15 right c 2right d g left e NOTA 44 If cos m n and sin m k then a cos7m in and sin7m 7k b cos7m n and sin7m k c cos7m in and sin7m k d cos7m n and sin7m 7k 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 fl l a Not enough information b 24 c 22 d 14 e NOTA 46 Find exactly sin391 It 27139 7r 27r a 7 b 7 c 7 d 7 e NOTA 3 3 3 3 47 Find exactly cosi1 75 7r 7239 7r 7239 a 7 b 7 c 7 d 7 e NOTA 6 6 3 3 48 In AABC A 400 a 26m B 600 Find b a 35m b 39m c 19m d 27m e NOTA 49 In AABC a5 b 3 ft C 680 Find c Round to two places a 4524111 b 227ft c 673ft d 477ft e NOTA 50 Solve sinx 5 on 0 27 a E is the only solution b g is the only solution c z 51 d z 2 6 6 3 3 e NOTA 51 What is the range of y sin x a 711 b 0271 0 H1 71 d 70000 e NOTA 52 What is the range of y sini1 x a 0271 b 111 0 071 d e NOTA 53 What is the range of y tani1 x a 70000 b 0 27 c 0 n d e NOTA 54 y gx is periodic with period 5 g6 1 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 7300 degrees b 500 degrees c 150 degrees d 371 2 Find x and y 20 cm 200 700 y x 3 Find 6 and x 10 cm 25quot 9 15 cm x 4 Find at and x 15 cm 0c 610 20 cm x 5 Use the fundamental identities to nd the exact value of sin x csc x and tan x given that 2 cosx 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 8 Find the exact value of sin 9 Find the exact value of cos For Problems 10 11 and 12 find one solution analytically then find other solutions by any method 10 44 7 32 cosl2x 51 on the interval 0 10 11 27 tan2x 765 on 0 50 12 500 25 sin52x 512 on 0 12 13 Angle A 2 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 7 14 Repeat for angle B 15 Repeat for angle C 16 Find a possible formula for each gmph a b 17 Simplify each expression by WIiting it Without using any tIigonometIic functions Find an exact Value Whenever possible a sin391 sin 6 b sinsin715 c sincos710 d sincos71x e 12nsin71x 18 a b Find a possible formula for each data table x 0 1 2 3 4 y 6 2 4 6 x r 0 7239 2 y Unde ned 0 Unde ned 0 x 1 05 0 05 1 15 y 10 7 10 13 10 7 19 A sine function y f x has a period of 8 and amplitude of 3 It is also known that f 2 18 is a minimum value of the function a b c d 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 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 b a 617 in b 1152 in c 1741 in c a5ftb7ftC 78deg d a10m b6mB 25deg e a5cm b6cmB 35deg fA40degB50degc6ft 21 a on the given axes make asketeh ofy cosx b Indicate on the giaph approximate solutions to cos x 74 c For each solution indicate the eonesponding quadrant ofthe unit circle 22 Repeat 21 withy sin x and sin x 77 u 23 A cosine function y gx 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 function Explain

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