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# Precalc AlgebraTrigonometry MAC 1147

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This 9 page Class Notes was uploaded by Duane Bayer on Wednesday September 23, 2015. The Class Notes belongs to MAC 1147 at University of South Florida taught by Sean McAveety in Fall. Since its upload, it has received 90 views. For similar materials see /class/212638/mac-1147-university-of-south-florida in Calculus and Pre Calculus at University of South Florida.

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Date Created: 09/23/15

MAC1147 Final Exam Review The following questions will help you prepare for the Final Exam It is safe to assume that if a topic is not present on this review7 then the topic will not be tested on the nal exam A formula sheet is attached at the end of this review It is the same sheet that will be on your nal exam A blank unit circle is also attached7 for your convenience Study well and good luck Trigonometric Functions 1 F 9 7 9 Write each of the following in radian measure a 45 b 7210quot c 480 Write each of the following in degrees a 3 b 51 c 7 If the radius of the circle is 3 rneters7 what is the length7 in rneters7 of the arc that is intercepted by a central angle of 25quot Each ofthe points below is on the terminal side of an angle 9 Find the six trigonometric functions of 9 a 37 5 b w 71gt Find the exact value of each expression a cos sin b sinvr 7 cos c 2sing 7 4cos7r Find the reference angle for each angle a 315 b 510 cgt d 107 7 Find the exact value of each expression a cos 120 b secT c tan 55 8 Find the exact value of each expression a Find cost if sint g and cost lt 0 b Find sect if tant 73 and sec gt 0 c Find sect if sint 7 and cost lt 0 9 Find the amplitude7 period7 and phase shift of each of the following functions a y 3sin x 7 b y 76 cos 2 c y 72 cos Bx 7 d y 5sin lt3 Write the equation of the sme function that has an amplitude of 3 and a period of 4 Write the equation of the cosine function that has an amplitude of 5 and a period of 3 H 3 Find the exact value of y a y cos l b y tan l 7Q 00 c y sin 1 sin 4 d y cos l cos e y sin cos 1lt f y tan sin 1 7 Trigonometric Identities and Trigonometric Equations 1 Simplify each expression a secs 71secz 1 7 tanzx 1 1 b csc17 cscs 71 2 Verify each identity 1 1 7 2 a17cosx Jr1cos 72030 b cos4x 7sin4z 1 7 2sin2 3 Find all solutions in radians for each of the following equations a sinx 0 b cot3 c cos 7 4 Find all solutions of each equation in the interval 07 27139 a sinltxgt b x3tanltz7gt710 A 1 c s1n3z7 d 2cos13tanx710 e 4cos2 f 2sin2z7cosx710 5 Find the exact value of each expression a sin45 30quot b tan 225 57139 c cos7 d cos 57 cos 33 7 sin 57 sin 33 e sin cos 7 cos sin 6 Find the exact value ofthe expressions below given that cos Oz 7 with 04 in quadrant 117 and sin 7 with in quadrant IV a cosoz 7 b sina 7 7 Find the exact value of each of the following trigonometric equations a sin 20 if sin g with 9 in ll b cos 261 if cost 71573 with 9 in III C tan2 iftan 4 and sin l lt 0 d 2 cos2105 7 1 2tan 75 8 1 7 tan2 75 f 17 2sin2165 Triangles H The angle relative to the horizontal from the top of a tree to a point 110 feet from its base on at ground is 15 Find the height of the tree to the nearest foot E0 At a time when the suns rays make a 50 angle with the horizontal7 how long is the shadow cast by a 6 foot man standing on at ground 9 Solve each of the triangles below 40 B 35 a 100 meters 110 O 46 70 235 feet 40 a 23 20 aA B A d B64 b45c60 B a b b O 46 b 35c 40 141 100 75 540 36A 792 D f E Polar Coordinates 1 Plot the following polar coordinates a 27 7 b 27 7 2 Convert each of the polar coordinates below into rectangular coordinates a 72300 b 5 3 Convert each of the rectangular coordinates below into polar coordinates a 17 1 b 72 2 4 Convert rectangular equation into polar form a 2 12 16 b z2y274x6y 12 5 Convert each polar equation into rectangular form a r2 b 97 03b Systems of 2 Variables 1 Solve the system given by 3x y 2 15x 5y 15 2 Solve the system given by z 7 3y 71 2x 7 3y 7 3 Solve the system given by z y 3 2x 2y 6 Partial action Decomposition 1 Write the general form of the partial fraction decomposition for each of the rational expressions below Do not solve x a x 1m 7 3 b 273z3 z1x27z1 2 Find the partial fraction decomposition for each of the rational expressions below a 2 l x 1 2 3x 2 b HQ 1 Conic Sections 1 Find the focus7 directrix7 and vertex of each of the following equations a 2 16y b y71221 0 96 i 32 4y 1 2 Find the standard equation of each of the parabolas described below a Focus 27 0 and directrix z 3 b Vertex 273 and directrix y 4 3 Find the vertices7 foci7 length of a major axis7 and the length of the minor axis for each ellipse 4 Find the standard form of the equation for the ellipse satisfying the given conditions a Foci i170 Vertex 30 b Center 17 74 major axis is vertical and has a length of 87 minor axis is horizontal and has a length of 6 5 Find the foci and the vertices for the hyperbolas below 2 2 z y a1 1 2 2 1 z b m m4 Sequences and Series 1 Find the fourth term of the sequence whose general term is given by an 231 71 2 What is the third term of the recursively de ned sequence where 11 747 and an 73a 7 57 9 r U 03 5 Find the general term7 an7 for the arithmetic sequence with the speci ed terms a 3rd term is 15 and the 21st term is 87 b 7th term is 8 and the 15th term is 8 Find the sum of the rst 7 terms of the given arithmetic sequence a 27 77 127 50 b 715 711 i7 n 20 Find the general term7 an7 for each of the geometric sequence below a 73 i6 712 724 b 13927 Find each nite sum 13971 a 2 G 8 2 H b 211 3 3 Find each in nite sum a g b 221 42quot 1 Some Useful Formulas sinu i 1 sinucosv j cosusim cosu i 1 cos u cos 1 I sinu Sim tanu i tanv t i1 7 anw 11 tanutanv sin 26 231n cos COS2 cosz isinz 172sin2 200s2 71 t 26 2tan an litan2 ii 170036 s1n27 1 2 COS i l1cos 2 2 tan i 170039 2 1COS nm 2 J

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