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Unformatted text preview: Math 113 Final Exam, Dec. 20, 2005, (60 minutes). NAME: ’ ‘ SECTION: Instruétor: TO RECEIVE CREDIT FOR AN ANSWER,
YOU IMUS’};1 SHOW WORK JUSTIFYING THAT ANSWER. I. (N0 CALCULATOR) 1) {10 points)The graph of y = 2003(33: + C) + D (with
B > 0) is shown below. Find the exact values of B , C, D. g/ 3 2) (10 points) Sketch the graph of y z —— sin(2:z:  §) for —7r 3 x 3 71’, including all exact values of y intercept and :v intercepts. ‘ _ Sin :8 below. 11. (N0 CALCULATOR) .
1) (5 points) Find the exact value of iBC‘l. 3)7(5 points) Find the exact value of a. 2) (5 points) Find the exact value of the area, of shaded region. 4) (10 points) A bicycle is traveling at 10 feet/second. Find the exact value of the speed
of its wheels measured in revolutions/ second, asSuming the diameter of wheeis is 2 feet. ‘ 111. (N0 CALCULATOR) 1) (10 points) Find the exact value of c0875“. 3) (15 points) Let 0033: = g— with 9% g a: 5 6w. Find the exact. value of cos IV. (15 points) Yeti wa
Assume that the water ﬂows 10 miles/hour from north to south. The boat travels relative to the water at 30, miles/hour.
You destination is at, the direction of southeast (Le. 845033). Find the heading of the boat and the speed of the boat relative. to the bottom of the river. V. (10 points) After seeing the top of the building at an angle of elevation of 30" you
wa'Iked toward the building for 100 feet and then saw the top of the building again at an angle of elevation of 45".
Find the height of the building. VI. (NO CALCULATOR) Prove or disprove the follbwing identities.
1) (5 points) For all a: with sin(2:c) ¢ 0,
cos(2m) 1 t =7 .
sin(2:z:) + aux sin(2x) 2) (5 points) For all x, Sin(7r + 23;) :: sin(2;v)  (cos(2m))(sin as). VII. (20 points), The, ﬁgure below shows 3 weights hanging with 2 pulleys. (The system is supposed to be “ideal”: weightless cables Without rigidity etc.)
With the quantities as shown, ﬁnd the values of oz and W3. (USE CALCULATOR) I VIII. (1) (7 points) Find (*1 + 7;)”. (Your answer should be in the rectangular form.) (2) (N0 CALCULATOR) (8 points) Find aﬂ solutions 2 to 232—34. (Your answer, should be in the trigonometry form.) 1x. (NO CALCULATOR) A force ? is appiied to a ball as shown below. The weight
of the ball is 10 lbs. (Assume that the incline is “idea ”: no surface friction etc.)
(1) (5 points) Find the exact value of the (minimum) force '17} that is needed to slide the ball along the slope from A to B, if 7?, assuming and the horizontal form an angle of
75°. 9 iprcl :l'o eéeef ) force VP? in‘U) to (2) (5 points) Find the exact value of the work done by the (minimum
slide the ball from A to B aiong the surface. X. (NO CALCULATOR) (15 points) Recall that 3:0 {or 0x0) stands for the direction measured as 2: degrees clockwise from north.
L An airplane is ﬂying on a heading of 030°
from northeast at speed of 40 miles per hour.
Find the ground speed and course of the airplane. at 208 miles per hour. The wind is blowing 10 ...
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 Spring '07
 ROSAY
 Trigonometry

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