Mock Examination III MTH_112 Elementary Functions

Transcription

1 Mock Examination III MTH_112 Elementary Functions Form a group and select at least one problem from this list. Prepare an oral report that describes a solution to your selected problem(s). Deliver your report as an interesting and enlightening mini-lecture. Your presentation will be peer marked and counts for 20% of your examination score. Criteria for marking your group s Mock Exam Analysis Report are: Preparation: The lecture was well prepared and thoughtfully organised. Report Format: The analysis report satisfied the course notation requirements and was clear, logical, and easy to follow. Technical Merit: Analysis conclusions were clear, concise, and technically correct. Pedagogical Value: This report prepared me for this type of problem should it appear on the coming examination. 5 December 2018 Kidoguchi, Kenneth

2 1. Co-terminal Angles (Angular Coincidence) Arredondo; Hector Bruhn; Nolan Irvin; Tyler Whisler; Jacob You are on Nobikini Atoll, a Pacific island on the Figure 1 earth's equator. You must transmit signals to a satellite that is in a circular orbit about the earth's equator as indicated in Figure 1. The satellite maintains a constant altitude above the earth's surface and orbits the earth every 40 hours. The satellite can receive signals from your transmitter only when it is directly above you. Assume that the earth is a perfect sphere and that the satellite will be directly above you at noon on 05 December Present the analysis to determine the time of the day and date on which your next two transmissions should occur. Transmission Time of Day (24 Hour Clock) Date (DD-MM-YYYY) 1 12: December Kidoguchi, Kenneth

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4 2. Triangles Not Selected A tower with a vertical height of h = 500 feet is to be erected on the side of a hill that makes an angle a = 15 o with the horizon. Two guy wires are to be connected to the top of the tower and secured at two points that are b = 500 feet directly above and directly below the base of the tower. Present the analysis to determine the length of each of the two guy wires in feet. Report lengths as exact values and lengths rounded to the nearest foot. h a 5 December Kidoguchi, Kenneth

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6 3. Graphing a Sinusoidal Functions Dunlap; Sam Judge; Peter Given: y = f(x) = 4 sin(2 x + p/3) + 100, a) Rewrite f(x) in the form y = A sin ω x ϕ ω + B. b) Use the ENTIRE grid provided below to sketch a properly labelled graph of f(x) on the interval ϕ, ϕφ + 2π 2π. ω ω ω ω ω ω φ 5 December Kidoguchi, Kenneth

7 4. Solving Trigonometric Equations Alarcon; Daniel Crow; Charlotte Deuna; Hayden Present the analysis to find exact values for the given angles on the interval [-p, p] that will satisfy each of following equations. a) cos(2a) = sec 2 (a) tan 2 (a) + e ip a = { } b) 2cos 2 (q) = csc 2 (q) cot 2 (q) q = { } c) cos 2 (b) sin 2 (b) = e ip/2 + e -ip/2 b = { } 5 December Kidoguchi, Kenneth

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11 5. Polar Coordinates (Sheet 1 of 2) Alarcon; Daniel Crow; Charlotte Deuna; Hayden Complete the table by matching the given polar equation with its polar plot. Polar Equation Polar Plot r 1 (q) = 2 + e ip 3 sin(q) r 2 (q) = 3 (cos 2 (q) - sin 2 (q)) r 3 (q) = 1+ 4e ip sin(q) r 4 (q) = 3 sin(q) ( e iq + e -iq ) ) ) i N. B.: Uncle Euler says: e q cos q + isin q 5 December Kidoguchi, Kenneth

12 5. Polar Coordinates (Sheet 1 of 2) Alarcon; Daniel Crow; Charlotte Deuna; Hayden Polar Plot A Polar Plot B Polar Plot C Polar Plot D 5 December Kidoguchi, Kenneth

13 6. Fun With Complex Numbers! Bates; Jason Kinjo; Eiichiro Liechty; Sarah Grace Rubbert; Sean Given the complex numbers: z i and z 1+ i Present the analysis to: a) Locate z 1 and z 2 on the complex plane using big dots and proper labels. b) Find: r 1 = z 1 and r 2 = z 2 c) Express z 1, z 1 ҧ, z 2, z 2 ҧ, in complex polar form (i.e., in the form z = r e iq ). (N.B. z 1 ҧ and z 2 ҧ are complex conjugates of z 1 and z 2 respectively. d) Evaluate z = (z 2 / z 1 ) 6 and express z in simplified rectangular form. 5 December Kidoguchi, Kenneth

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15 7. Vector Plug-n-Chug Bates; Jason Kinjo; Eiichiro Liechty; Sarah Grace Rubbert; Sean Given Ԧv = 1, 1 and w = 1, 1 : Ƹ Ƹ a) Sketch the vectors Ԧv, w, Ԧr = Ԧv + w, and റs = Ԧv w on the grid provided. b) Compute the magnitudes of each vector: Ԧv = w = Ԧr = Ԧs = j c) Compute unit vectors for each vector: v = i w = r = s = d) Compute the dot product റv w and explain what it means. 5 December Kidoguchi, Kenneth

16 8. Vector Analysis Arredondo; Hector Bruhn; Nolan Irvin; Tyler Whisler; Jacob Kayakers paddle due east on a straight river that passes a famous landmark. At noon their bearing to the landmark is N75 E. Thirty minutes later, after paddling 5 kilometres farther, their bearing is N45 E. Present the analysis to find vectors in proper vector notation with exact values that point from the kayak to the landmark at: a) noon, b) at 12:30, and c) when the kayakers are at their closest point to the landmark as they paddle along the straight river. N N N E a b a = 75º b = 45º 5 December Kidoguchi, Kenneth

17 N N N E a b a = 75º b = 45º 5 December Kidoguchi, Kenneth

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