Math 1022 Final Exam Name Fall 2000 Page 1 of 7 You must show your work If more space is needed you may use the back of the page You may use a scientific calculator on any problem However if a problem states that your answer must contain exact values a decimal approximation will not be accepted The point total for each problem is listed in brackets above the problem It is not necessary to reduce fractions add multiply or divide fractions rationalize denominators or simplify radicals 12 1 Find the value of each expression correct to 3 decimal places If the value is undefined state so a sin 220 130 a b cot 5 2 b c cos 1 3 c 8 2 Suppose 7 12 a Express in exact degrees a b Find the reference angle for in exact radians b 6 3 Find the linear velocity of an object traveling around a circle of radius 35 inches if a central angle of 13 radian is swept out in 40 seconds 3 12 4 Solve the right triangle shown below Round to one decimal Use degree measure c Math 1022 Final Exam Fall 2000 Page 2 of 7 27 5 Sketch at least one period of each function Label x intercepts and any asymptotes a y 3 cos x 4 b y sin 1 2 x c y 1 tan x Math 1022 Final Exam Fall 2000 Page 3 of 7 32 6 Find the EXACT value answer s for each of the following a Use the sum formula for sin x y to find b Use the half angle formula for cos x 2 to find c If tan 34 and is in quadrant 2 find d State the domain and range of the function sin 195 a cos 105 b sin 2 y cot x c d Domain Range e If cos 23 then what is cos f Find sin 1 sin h g Find cot sin 1 6 i 3 2 e f g h Find the area of the equilateral triangle having sides of length 4 h Math 1022 Final Exam Fall 2000 Page 4 of 7 18 7 Verify the following identities sin a cos 3 2 b cot2 x 1 1 2 sin2 x 2 1 cot x 7 8 A spotlight covers a circular area It has a range of 200 feet and sweeps out an angle of 45 What is the area of the land it can cover Round to the nearest square foot 8 Math 1022 Final Exam Fall 2000 Page 5 of 7 27 9 Solve each equation for x where 0 x 2 Find the EXACT values for the answers a 2 sin2 x sin x 1 0 a b tan x 1 2 sec x 1 0 b c cos2 x 1 4 c 9 10 Find ALL solutions in radians correct to 3 decimal places for the equation 10 sin x 0 89 Math 1022 Final Exam Fall 2000 Page 6 of 7 10 11 Two guy wires for a radio tower make angles with the horizontal of 58 and 49 If the ground anchors for each wire are 150 feet apart find the length of the longer wire Round to the nearest tenth of a foot 11 10 12 Two ships leave port at the same time One travels in the direction N35 E at a rate of 25 mph The other travels in the direction of S70 E at a rate of 30 mph How far apart are the ships after 2 hours Round to the nearest tenth of a mile 12 Math 1022 Final Exam Fall 2000 Page 7 of 7 8 13 Find the coordinates of two polar points one with r 0 and one with r 0 equivalent to the rectangular point having coordinates 1 3 13 6 14 Given the polar points A 4 4 B 2 C 3 4 3 plot and label each point 8 15 Sketch the graph of the polar equation r 3 3 sin and label at least 3 points