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Test_3B

# Test_3B - 0 ﬂ'0 Fa112007 Math 151 Test 3B Name i 2 é a...

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Unformatted text preview: \ 0 ﬂ '0 Fa112007 Math 151 Test 3B Name i 2% é a! 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. 1. (20) means problem 1 is worth 20 points. i. This test is to be completed in one hour and ﬁfteen minutes. mwogocp On my‘honor, l have cleared all functions from my calculator and have neither given nor received help on this test. Pledge (Sign your name) 5 1. (10) If the tan 6 = — and cos 6 = —2, ﬁnd the value of the remaining four ‘ -— 12 “—— 13 trigonometric functions. Egg-3‘6: -5z3 csc6: ’315' wt ”/5. ' _ :3 m9: [2. 2. (10) . The terminal side of an angle 6 in standard position lies on the line, y : —%x in the second (2nd) quadrant. Find the exact simpliﬁed values for all six trigonometric functions for the angle 6. Be sure to draw and label a sketch showing the speciﬁc quadrant 6 is in. 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 10:55 am. Use either 5 = r6 orA =lr26 , whichever is appropriate. 2 Leave your answer in terms of 7r. b. Determine the linear velocity of a point moving on the tip of the minute hand. . s . . . . Use either 5 = r8 or v = —, whichever is appropriate. Leave your answer in Z terms of 7:. 4. (15) Given the following right triangle where angle A =41O 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 th) of an inch. 0 AB = W"! €99 B sideb= [35.ﬂw'. . /§ Sidec — ‘19: Q n. , c//V9 +-~ W 73; .«4’24. [3: NEW L190 '_ 0 Lil 5. (10) Find the exact value of the expression cost?) — sin [7%]. To receive full credit you must use a properly labeled sketch with angles located in the correct quadrant. .L 2. " O . l . 6. (10) Given tan 6’ = —— and cos < 0 Find the exact values for sin6 and sec 6. To 3 receive full credit you must include an appropriately labeled sketch located in the appropriate quadrant. sint9= FIE—(2° sec6= -! 2° 3 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. 7714...” Maggi-5&0 0L "- aroma 8. (10) Find the angle of elevation of the top of a 35—foot building at a horizontal distance of 52 feet. 2 —r— -— #— ﬁ 9(\ as 5 “I E 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. V 10. (10) For the graph of the equation, y = —2 cos£3 [x —2—7ZD +1 , state the following. 3 (Do not graph) Show the work used to determine the period and the phase shift. . . 9.7!" a. Amplitude . QM “pat :: T b. Period «:11 3 0. Phase shift .21 d. Vertical shift (a? l 11. (15) Evaluate the following expressions. To receive full credit you must use a pr0perly labeled sketch with angles located in the correct quadrant. a. cos(cos'1(—2)) THE 3 b. cos(sin_1 (—1?) 71 1 12. (15) Write the equation of a sine function y = a sin(b(x — 0)) + d that has the following characteristics: Amplitude: 5 (3" 53011-6? 6H 31)) -4f Period: 67\$ Phase Shift: ”’5 3 Vertical shift: down 4 units 13. (10) ' Verify the identity: 1 1 + = 2csc2 x 1—cosx 1+cosx ...
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