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# math 101 Physics 1250

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This 8 page Class Notes was uploaded by Celine Notetaker on Thursday August 11, 2016. The Class Notes belongs to Physics 1250 at Ohio State University taught by Staff in Fall 2016. Since its upload, it has received 5 views.

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Date Created: 08/11/16

MSLC – Math 1149 Final Exam Review Disclaimer: This should NOT be used as your only guide for what to study. 1. In the circle pictured below, r is the radius of the cirlis the central angle of the sector, A is the area of the sector, and s is the length of the arc subtended by the central angle. Find: a. A and s if r 3 inches, and radians 3 b. r and s if A 2.25 square miles, and 36 c. A and ifr 4 meters, and s 12.57 meters d. r and A if s 13 meters, and radians 4 2. Use the given information to find the exact value of the six trigonometric functions of the ange in the picture. a) a 8 b 15 b) a 12 c 13 2 c) sin 7 d) cot 3 3 e) cos 5 f) csc 5 3. For each part, determine the quadrant lies in and the values of the five remaining trigonometric functions. a) csc 65 and cot 0 13 b) sec 4 3 and sin 0 c) tan 35 and cos 0 12 4. Find the exact value of each of the following. 1 99 a. tan in 101 1 4 b. cos cos 3 5. Given triangle with the following properties: ABC b 14, c 17, B 44 and C is an obtuse angle Find the measure of angle C. Round your answer to 2 decimal places. 6. Given the following graph, find an equation that will satisfy the given conditions. a. y acosk x b b. y asink xb c. y acosk xb 7. Find the period, amplitude, and phase-shift of the given trigonometric equation, then graph one complete period. a. y 3sin b. y 2cos4 x 6 c. y 5sin 2x 4 8. A team of surveyors have been hired to measure the distance across a canyon. Using a tree at point T on the opposite site of the canyon as a reference point, they established points A, B, and C and found the following distances: AB = 12.25 ft BC = 6.5 ft AC = 15 ft a. Find the measure of angle ABC. Round your answer to 2 decimal places. b. Find the distance TC across the canyon to the nearest foot. 9. Establish the identity: 1sin x 2 a. 1sin x sec x tan x b. sec csc sin cos tan cot c. sin xsin x 2 2 1sin2x 1 d. 1 sec xcsc x sin2x 2 10. Find the exact solution of: 11 a. sin 12 b. tan(165) 7 c. cos 8 11. Find all solutions of: a. 2cos2x1 0 on the interval0,2 b. cos xsin x 2cos x 0 x c. 2sin 2 3 0 on the interval ,8 2 12. Given cot x and sin x0 find: 3 a.sin2x x b.sin 2 c.cos2x x d.cos 2 3 3 3 2 2 13. Given the complex numbers 1 i and z2 i 2 2 2 2 a. Convert both z and z to polar coordinates 1 2 b. Find z1 2 z c. Find 1 z2 1 d. Find z1 7 14. Use DeMoivre’s Theorem to find z in the standard a bi form: a.z 1 i b. z 3cos isin 6 6 15. Given u 2ij andv 3i2j find: a.u v b.3u 4v c. u v d. 3u 4v e.uv f. the angle (in degrees) between u and v. Round your answer to 3 decimal places. 16. a. Find the equation of the parabola with vertex at the origin and a directrix ox 6 b. Graph the parabola, making sure to plot and label all information given in part a. 1 17. a. Find the equation of an ellipse with eccentricity o9 and foci at0,2 b. Graph the ellipse, making sure to plot and label all information given in part a. 18. a. Find the transverse axis, vertices, foci, and the equations of the asymptotes of the hyperbola 2 2 described by the equation 9x 4 y 36 . b. Graph the hyperbola, making sure to plot and label all information given in part a. ANSWERS 1. a. s 3.142 inches A 4.712 in2 b. r 2.676 miles s 1.681miles 2 2 c. (radians) A 25.13 m d. r 16.552 meters A 107.589 m 8 15 8 17 17 15 2. a.sin cos tan csc sec cot 17 17 15 8 15 8 12 5 12 13 13 5 b.sin 13 cos 13 tan 5 csc 12 sec 5 cot 12 2 45 2 7 7 45 c.sin 7 cos 7 tan csc 2 sec cot 2 45 45 1 3 1 10 d.sin cos tan csc 10 sec cot 3 10 10 3 3 4 3 4 5 5 3 e.sin cos tan csc sec cot 5 5 3 4 3 4 1 2 1 5 f. sin cos tan csc 5 sec cot 2 5 5 2 2 1 8 1 3. a. is in Quadrant III sin ; cos ; tan 65 65 8 65 csc 65 sec cot 8 8 b. is in Quadrant II sin 11 cos 48 tan 11 13 13 48 csc 13 sec 13 cot 48 11 48 11 35 12 35 c. is in Quadrant IV sin 37 cos 37 tan 12 csc 37 sec 37 cot 12 35 12 35 99 2 4. a. b. 5. C 122.49 20 3 6. a. f cos x b. g 2sin2 x c. h 7cos 2 8 6 7. a. Amplitude: 3 Period: 2 Phase-shift: none b. Amplitude: 2 Period: Phase-shift: 2 6 c. Amplitude: 5 Period: Phase-shift: 8 8. a. ABC 101.84 b. TC 31feet secxcscx 1sin x ec x tan x2 sin xcos x 1sin x tan xcot x 1 1 1sin x·1sin x RHS 1sin x 1sin x cosx sin x RHS 2 sin x cos x 12sin x sin x RHS cosx sin x 9. a. 1sin x b. 12sin x sin x sin xcos x RHS cosxsin x cos x sin xcos x2 RHS 1 2sin x sin x RHS cosxsin x cos x cos x cos x sin xcosx cosxsin x sec x2sec xtan xtan x (sec xtan x) 2 · 2 2 sin xcos x cosxsin x sin xcos x ______________________________________________________________________________ sin xsin x 2 2 1sin2x 1 secxcscx sin2x 2 LHS sin cos sin xcos sin2x 1 2 2 RHS sin2x sin2x c. LHS 1cosx0 d. 1 LHS cosx 1 RHS 2sin xcosx sin x cosx 1 1 2 1 cscxsecx 1 secxcscx 2 2 ______________________________________________________________________________ 6 2 1 3 2 2 10. a. b. c. 4 1 3 4 3 5 11 13 2 4 14 16 11. a. , , , b. k c. , , , 8 8 8 8 2 3 3 3 3 12 1 1 5 1 1 12. a. b. c. d. 13 2 13 13 2 13 13. a.z 1, 3 or ,135 ; z 3, 4 or ,240 b. 3 cos 25 isin 25 1 4 2 3 12 12 c.3 cos 7 isin 7 d. 1 cos4 isin4 12 12 3 3 3 14. a.88i b. 2187 3 2187 i 2 2 15. a.5i j b. 6i11j c. 26 d. 157 e. 4 f. 60.255 2 2 16. y 24x 17. x y 1 320 324 18. Transverse axis: the x-axis;Vertices: 2,0; Foci: 13,0 ; Asymptotes: y 3 x 2

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