Tuesday, May 2, 2006

Transcription

1 Final Exam MTH, Section # Tuesday, May, 006 Name (Print) Signature PID# DO NOT BEGIN THIS TEST UNTIL YOU ARE TOLD TO DO SO. This exam consists of multiple choice questions and open-ended questions on pages, including this front page and formula sheet. Turn in all pages of this exam. Circle the letter of the correct answer for multiple choice questions #-. Write your answers on the line provided for open-ended questions #3-3. Show your work for open-ended questions #3-3!!! NO WORK = NO CREDIT! You must show work that supports your answer in order to get credit. Be neat and orderly. For problems asking for EXACT answers, leave in terms of fractions, and number. For decimal answers, round to decimal place unless otherwise specified. Give measurement units (feet, degrees, etc.) when appropriate. # Score Possible # Score Possible - x6= TOTAL 00

2 Multiple Choice Questions Circle the letter of the correct answer. 6 points each.. Find the exact value of csc 3 a) b) c) 3 d) e). Find the exact value of tan 7 tan. a) b) c) d) 3 e) 7 3. Two coterminal angles of are: a) 7, b), c) 3, d) 6,. The reference angle for θ = 9 is: a) -9 b) c) 88 d) 78 e) 68

3 . The polar form of the rectangular equation x + y - 7x = 0 is: a) r = 7cosθ b) r = 7sinθ c) r = 7rcosθ d) r = 7x e) x + y = 7rcosθ f) None of these. 6. Match the graph with the correct function: /6 /3 / /3 /6 /6 /3 / /3 / a) cos 3x b) -sin x c) sin + x 3 3 d) cos x e) -sin 3 3x f) None of these The minute hand of a clock is 6 inches long. How far does the minute hand move in minutes? 6 a) inches b) inches c) inches d) inches e) inches 3

4 8. The largest angle of a triangle with sides, 7 and 9 is approximately: a) 0 b) 73. c) 90 d) 06.6 e) 63. f) Not enough information. 9. A triangular garden plot has sides meters and meters with the angle between the sides measuring. What is the approximate area of the garden? a).3 m b). m c) 6 m d) 8. m e) 9. m 0. A polar representation of the rectangular coordinates ( 3, ) is: a) (, ) b) (-, ) c) (-, 3 ) d) (-, ) e) None of these.. When tuning a piano, a technician strikes a tuning fork for the A above middle C and sets up a wave motion approximated by d = 0.00sin 880t, where t is in seconds. The frequency (in cycles per second) of this note is: a). 00 b) 880 c) 0 d) 0 e) 880. If cosx =, then cos(x - ) is: a) 6 b) 6 c) d) e) 6

5 Open-ended Questions Points for each question are labeled. Show your work, give EXACT answers when requested. 3. (0 points) Determine the period, phase shift, vertical shift, and range for the x +. graph of y = - - 3sec ( ) 3 Period = Phase Shift = Vertical Shift = Range =. (0 points) Solve the triangle(s). a = B = 36º b =.

6 . ( points) Verify the identity. Work on ONE side only: sec ( ) cscx + sin( x) x = tan x 6

7 6. (8 points) Find the EXACT value of csc tan ( points) Plot and label the following polar coordinates. Convert the points from polar to rectangular coordinates (Exact values). a. (, ) (, ) 6 b. (, ) (, ) c. ( 3, ) (, ) 3 7 d. (, ) (, ) 7

8 8. (8 points) Find all EXACT solutions of x in [0, ): cosx = ( points) Find all GENERAL solutions for x: tan x + secx = Give algebraic solutions only, EXACT if possible. Round all other solutions to decimal places. 9. 8

9 3 0. (6 points) Given csc u = and < u < and cot v = 3 with sec v < 0, find the EXACT value of: a. sin (u - v) u b. cos. ( points) An observer s eye is 6 feet above the floor. A painting is being viewed. The bottom of the painting is at floor level. The angle of depression from the observer s eye to the bottom of the painting is and the angle of elevation from the observer s eye to the top of the painting is 8. How tall is the painting? [Draw a fully labeled diagram of the given information as part of your answer.]. 9

10 . ( points) If you are on island C, what bearing should you navigate to go to island A? C miles 7 miles A 6 miles B. 3. ( points) MaCherie is driving north along a straight road in central Colorado. She looks out the left window of her car and sees Long s Peak at a bearing of N W. After traveling at miles per hour for minutes, she looks out the window again and sees Long s Peak at a bearing of N30 W. How far was MaCherie from Long s Peak at the first sighting? [Draw a fully labeled diagram, showing bearings, as part of your answer.] 3. 0

11 Math Final Exam Tuesday, May, 006 Section # Name PID # FORMULA SHEET (Sum, Difference, Double and Half Angle Formulas Only) sin (u v) = sinucos v ± cos usin v ± cos ( u ± v) = cos u cos v m sinu sin v tan ( u ± v) = tanu ± tan v m tanu tan v tanu tanu = tan u sin u = sinucos u cos u = cos u sin u = cos u = sin u u cos u sin = ± u cosu sin u tan = = sin u + cosu u cos = ± + cos u