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Test_3A - Fall 2007 Math 151 Test 3A Name DO NOT TURN THIS...

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Unformatted text preview: Fall 2007 Math 151 Test 3A Name DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO START. Notes: Before you begin, write your name at the top of the page. To receive partial credit for a problem, you must clearly show ALL WORK All answers are to be completely simplified unless told otherwise. Do not ask the instructor how to do a problem; only ask about its legibility. You may use the back of these pages as scrap paper. Don’t forget to check your work for errors before you submit your test. All functions must be cleared from your calculator before you leave the room. Failure to do so constitutes an honor violation. Random checks will be performed by your instructor. h. This test is worth 150 points. The weight of each problem is indicated by a number within the set of parentheses; i.e. l. (20) means problem 1 is worth 20 points. i. This test is to be completed in one hour and fifteen minutes. mwsaocs» On my honor, I have cleared all functions from my calculator and have neither given nor received help on this test. Pledge (Sign your name) 7 24 l. (10) If the cot 6 = 2—4 and sin 6’ = —2—5, fmd the value of the remaining four 'tn'gonometric functions. 4 .. ‘1 r cos¢9= “#2; 0806?: /L'/ 2. (10) . The terminal side ofan angle (9 in standard position lies on the line, y = Ex in the third (3rd ) quadrant. Find the exact simplified values for all six trigonometnc fiific'fions for the angle (9. Be sure to draw and label a sketch showing the specific quadrant (9 is in. "‘ z .. F5"? sin6=qF csc6= /’7 #36"? 0080: 57 3606:” se;3 tant9= 0/3 cot6= 3&2 3. (10) A minute hand on a clock is 4 inches long. a. Determine how far the tip of the minute hand travels between 10:15 am. and 10:50 am. Use either 3 = r9 or A =lr2c9 , whichever is appropriate. 2 Leave your answer in terms of 7: 5:42:51? b. Determine the linear velocity of“, a point . s . . . . Use either s = n9 or v = —, whichever is appropriate. Leave your answer in t terms of 7r. 5914—:— L? _1__4-77 SS IOE 4. (15) Given the following right triangle where angle A= 410 and side a = 118 inches, solve the right triangle for angle B, side b and side 0. Round the sides to the nearest tenth (10 ’h 5. (10) Find the exact value of the expression cos[7—6fl] — sin [47”]. To receive full credit you must use a properly labeled sketch with angles located in the correct quadrant. . 1 , , 6. (10) Given tan 6’ : ~§ and cos < 0 Find the exact values for srn6’ and sec 19. To receive full credit you must include an appropriately labeled sketch located in the appropriate quadrant. sin 6: se06= 7. (10) From a ISO—foot observation tower on the coast, a Coast Guard officer sights a boat in difficulty. The angle of depression to the boat is 6°. How far is the boat from the shoreline? To receive full credit, a properly labeled sketch is required. Round your answer to the nearest foot. m0”) '-'-' 152')" 4a» fiat—L" M“ 0 I i '\ 8. (10) Find the angle of elevation of the top of a 35—foot building at a horizontal distance of 52 feet. 9. (15) A graph of a sine function is shown below. Using this graph, find the specific values of a and b then write the equation in the form y = a sin bx . Show all work ‘ used to calculate a and b. 10. (10) For the graph ofthe equation, y = 2cos[3[x——73:D + 3, state the following. (Do not graph) Show the work used to determine the period and the phase shift. a. Amplitude 9- b. Period 2:173 c. Phase shift i2; E d. Vertical shift AP 3 11. (15) Evaluate the following expressions. To receive full credit you must use a properly labeled sketch with angles located in the correct quadrant. a. cos(cos‘1(—3)) 3fi/‘£ b. cos(sin'1(l))' m (:gi = D C. sin—(00552} ._._ m" {-63 = ._ I 12. (15) Write the equation of a sine function y = a sin(b(x — c)) + d that has the following characteristics: . * 1—K Amplitudcz5 g:53w(3/ 1+3» ‘7‘ Period: 67: Phase Shift: —1 3 Vertical shift: down 4 units urn: Z-J. b curbs—Z” b-J-a 13. (10) ' Verify the identity: 1— cos x 1+ cos x ...
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