Review Sheet for TIB 104 at KU
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Date Created: 02/06/15
Math 104 Review Final Spring 2004 Show all work Answers without support will not receive credit Simplify all answers Answers should be exact unless otherwise stated 1 Put each equation below in standard form and determine which type of conic section it is Depend ing on what type it is nd the center vertices andor foci Sketch the graph a m 72x8y90 2 b 4m2y278m4y780 c 9x27y254m10y550 d y274x740 D gty ltz272z5gt f 9m274y236m724y360 g 16352 25g2 7 32 50y 16 0 h y2z274m6y75 2 Find the standard form for each of the following a Ellipse Vertices 73 0 7 0 Foci 0 0 4 0 b Hyperbola Vertices 22 72 2 Foci 4 2 74 2 3 Sketch the curve represented by the following parametric equations indicate the direction of the curve Then eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve a z372ty23t b mcos0y 3sin0 c mln2ty2t2 d z33cos0y25sin0 7 75 995 thy f m6cos0y6sin0 g zsec0ytan0 h m172sin0y2icos0 Math 104 Review Final Spring 2004 4 For the following polar coordinates7 nd the corresponding rectangular coordinates f 715 0 5 For the following rectangular coordinates7 nd two possible polar representations a 079 b 737 c 22 d 715 6 Convert each rectangular equation to polar form a m2y276m0 b 4x7y720 7 Convert each polar equation to rectangular form a r4cos0 757139 3 710 b 0 C d r2 3sin20 e rcos0r2sin0 f 4cos02sin0r Math 104 Review Final Spring 2004 8 Sketch the graph of the following polar equations a r6 57139 3 c r6cos0 we d r3cos50 9 The following parametric equations below describe the ight of a baseball 25 seconds after being hit7 where z is the horizontal distance from home plate in feet7 and y is the height in feet x 1391t y 3 562t716t2 a What is the height of the baseball when it is hit b What is the maximum height of the baseball c A 10 ft out eld fence is a distance of 400 ft from home plate Is the hit a home run 10 Find the amplitude7 period7 phase shift and vertical shift of the following and sketch a graph a gz cos3m 7 b f0 sin50 5 c ut 3 7 sint E d hz 2 5 cos8m 7 4w 7 11 Given sin0 7E and 9 is in Quadrant lV7 nd the values of the other trigonometric functions 12 The height of a radio transmission tower is 70 meters and it casts a shadow of length 30 meters Find the angle of elevation of the sun 13 Verify the identities a sec2 zcotm 7 cotz tanm b cos3 x sin2 z sin2 z 7 sin4 z cos x c 2 sin y cos y sec 2y tan 2y d sinu 12 cos u cos 1 tanutanv Math 104 Review Final Spring 2004 14 Find the exact value using the appropriate identities 57139 a sin7 12 b cos285 c cos 51 7 sin 39 15 Find all the solutions of the equation in the interval 07 27139 a sinz 7tanm 0 b sin2z sinm 0 c cos4z 7 7cos2m 8 d sin 4x 7 sin 2x 0 e 2sin2z7 0 f cos4zcosm 71 0 16 Use the given information to solve the triangles If two solutions are possible7 list each a B 110 a 4c4 b a5b8c10 c B 25 a 627 C 85 17 To approximate the length of a marsh7 a surveyor walks 25 meters from point A to point 13 Then he turns 65quot and walks 300 meters to point C Approximate the length AC of the marsh 18 A boat runs in a straight line for 5 kilometers and then makes a 45 turn and runs for another 6 kilometers How far is the boat from its starting point 19 The amount P in tons of pollution emitted by a certain factory is given by P 351 cos 7 where n is the number of weeks after January 1 Use inverse trigonometric notation to solve for n 20 Find equations for two distinct ellipses both of which have center at 27 767 major axis of length 127 and minor axis of length 8 Math 104 Review Final Spring 2004 21 Find the exact value of the following a cosarctan 2 4 b cosarcsin i 5 t if c s1narc an 12 d tanarcsin 71 22 A parabolic archway is 12 meters high at the vertex At a height of 10 meters7 the width of the archway is 8 meters How wide is the archway at ground level 23 You are building a wading pool in the shape of an ellipse Your plans give an equation for the 2 elliptical shape of the pool measured in feet as 3mm a 1 Find the longest distance across the pool 24 A plane ies 810 miles from A to B with a bearing of N 75quot E Then it ies 648 miles from B to C with a bearing of N 32quot E Draw a diagram to represent the problem and nd the straight line distance and bearing from C to A and u and v i i i i i i 3 5 25 Find the exact value of the trigonometric function given that sinu Z cosv 7E are in Quadrant ll 26 Use an inverse trigonometric function to write 9 as a function of z 16 x3 0 K a z1 0 K b 20 Math 104 Review Final Spring 2004 27 Solve 2lnm 7 ln5m 7 6 0 for z 28 Solve em3 53853 for z 29 Let x 55m and gz arcsinlnz Find f og2 30 An isosceles triangle has two equal sides of length 6 cm and the angle between the two equal sides is 45 Draw a picture of the triangle and nd the area