1MA 154 PRACTICE QUESTIONS FOR THE FINAL 8/031. If θ is in the second quadrant and sinθ = 0.6, find cosθ.A. – 0.75 B. 0.2 C. – 0.8 D. 0.8 E. None of these.2. The angles with measures listed are all coterminal except:A.π3B.−5π3C.−300°D.420°E.−60°3. The radian measure of an angle of 135° is:A.5π4B.3π2C.3π4D.7π8E. None of these.4. Use a calculator to find the sec 126° correct to 4 decimal places.A. 1.2361 B. – 0.5878 C. – 1.7013 D. – 1.2361 E. None of these.5. The point (12, – 16) is on the terminal side of the angle θ. Find tanθA.53B.−54C.43D.45E. None of these.6. If the diameter of a circle is 6 cm, find the length of the arc that subtends a centralangle of 30°.A. 1.571 cm B. 2.356 cm C. 3.142 cm D. 9.425 cm E. None of these.7. Find the area of a sector determined by θ in problem #6.A. 1.571 cm2B. 2.356 cm2C. 3.142 cm2D. 9.425 cm2E. None of these.8. Sketched below is a portion of the graph of which trigonometric function?A.y =12cos14xB.y = 4cos12xC.y =−12sin4 xD.y =12cos4 xE.y =−12cos14x9. The graph of y = 3 + sin x (Choose all the correct answers.)I. crosses the y-axis at 3 II. crosses the x-axis at multiples of πIII. is always above the x-axis IV. has period 2πA. I, II B. I, III, IV C. I, II, IV D. II, IV E. None of these.10. Give the domain, D, and the range, R, of f(x) = cos x.A. D = set of all real numbers, R=[–1, 1]B. D = [0, ∞), R = set of all real numbers.C. D = [0, 2π], R = [–1, 1]D. D = set of all real numbers, R = [0, 2π]E. None of these.π4π21– 1211. From a point P on level ground the angle of elevation of the top of the tower is 26°50′.From a point 25.0 meters closer to the tower and on the same line with P and the baseof the tower, the angle of elevation of the top of the tower is 43°30′. Find the height ofthe tower correct to one decimal place.A.39.3 meters B. 12.6 meters C. 27.1 meters D.23.7 meters E. None of these.12. The expression tan2x1+ secx is identically equal to:A. 1 B. sec x – 1 C. tan x + sin x D.tan2x + sinxtanxE.cscx+ sinx13. Simplify tanxcosxcscxcotxsecxsinx:A.tan2xcos2xB. 1 C.csc2xD. 0 E.tan2x14. Reduce to a single term: cos(2A) cos B + sin (2A) sin BA.sin (2A + B) B. sin (2A – B) C. cos (2A – B) D.cos (2A + B) E. None of these.15. Find all the solutions of 3cos2x+ 2sin x+ 2= 0in the interval 0,2π[ )A.x = 0,π2B.x =π4,π2C.x =π2D.x =π4E. None of these.16. How many solutions of the equation sin2θ = cosθ lie in the interval 0,2π[ )?A. 2. B. 3 C. 4 D. 1 E. None of these.17. Find cosθ in the figure given on the right.A.3720B.740C.516D.3740E. None of these18. Given cosθ =34 and 270° < θ < 360°, find sin2θA.−3 78B.− 74C.−18D.18E.3 7819. Which equation best describes the graph given below?524θπ– 2 2A.y = 2sin−1x( )B.y = cos−1x2      C.y = 2cos−1x( )D.y = sin−1x2      E.y = cos−12x( )320. Find the cos 2arcsin45            . Do not use a calculator.A.725B.−725C.3225D.−3225E. None of these.21. Point A is 2.0 miles north of B. The bearing from A to C is S 35° W and thebearing from B to C is S 86° W. Find the distance from A to C correct to onedecimal place.A. 2.6 miles B. 1.6 miles C. 1.5 miles D. 3.5 miles E. None of these.22. Find the magnitude of the vector 2,3A.6B. 6. C. 5 D.13E. None of these.23. If r a = 2,2 and r b = −2,3, the sketch below corresponds to:A. r a +r b B. r a −r b C. 2r a +r b D. 2r a −r b E. None of these.24. If 6.0 lb, 110° is the magnitude and direction of one force and 2.0 lb, 250° is themagnitude and direction of a second force, calculate the magnitude (to one decimalplace) and the direction (to the nearest degree) of the resultant.A. 4.6 lb, 126° B. 7.6 lb, 120° C. 6.9 lb, 126° D.6.9 lb, 120° E. None of these.25. Which equation best describes that graph given below?(6, 1)2 (6, 2)3(3, 4)xyA.x −6( )23+y− 4( )22= 1B.x −6( )29+y− 4( )29= 1C.x −3( )29+y − 2( )24= 1D.x −3( )24+y − 2( )29= 1E.x −2( )29+y− 3( )24= 1426. Classify the equations given below.I.x2− y2+ 2x =15II.x2+ 3y2+ 4x −2y − 5= 0III.x2− 4x+ y− 7 = 0A.I. ellipseII. parabolaIII. hyperbolaB.I. hyperbolaII. ellipseIII. parabolaC.I. parabolaII. hyperbolaIII. ellipseD.I. hyperbolaII. parabolaIII. ellipseE.I. parabolaII. ellipseIII. hyperbolaF.I. ellipseII. hyperbolaIII. parabola27. The graph of 9x2− 25y2= 225 most closely resembles which graph sketched below?A. B. C.D. E. F.28. Find the vertex of the parabola y2− 4y− 2x− 4 = 0A. (–2. 2) B. (–4, 2) C. (2, –4) D. (4, –2) E. (2, –2)-6-4-20246-15 -10 -5 0 5 10 15-10-50510-15 -10 -5 0 5 10 15-6-5-4-3-2-10123456-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-6-5-4-3-2-10123456-10 -8 -6 -4 -2 0 2 4 6 8 10-10123456789101112-5 -4 -3 -2 -1 0 1 2 3 4 5-12-11-10-9-8-7-6-5-4-3-2-101-5 -4 -3 -2 -1 0 1 2 3 4 5529. An arch of a bridge over a roadway is semielliptical with major axis horizontal. Thebase of the arch is 30 feet across and highest part of the arch is 10 feet above thehorizontal roadway. Find the height of the arch 10 feet from the center of the base.A. 9.4 feet B. 8.9 feet C. 7.5 feet D. 10.0 feet E. 9.9 Feet30. List all places where the graph of f(x) =x2−9x2+ 2x has vertical asymptotes.A. x = 0 B. x = 2 C. x = 0, x = –2 D. x = 3, x = –3 E. None of these.31. The graph of f(x) =x− 2x + 2 most closely resembles which graph sketched below?32. Find the reference angle for θ = –156°A. θR = 156° B. θR = 204° C. θR = 66° D. θR = 24° E. None of these.33. Find the reference angle for θ = 4π3A. θR = π3B. θR = 4π3C. θR = 2π3D. θR = −2π3E. None of these.34. Find all the values of θ in the interval [0, 2π) that satisfies the equation sin θ = –0.5873.Round your answer to two decimals.A. –0.63, 3.77 B. 0.63, 2.51 C. 3.77, 5.66 D. 5.34, 2.20 E. None of these.–1–22–1–212112A.B.C.D.E.6Answers:1 C 18 A2 E 19 B3 C 20 B4 C 21 A5 E (-4/3) 22 D6 A 23 D7 B 24 A8 D 25 C9 B 26 B10 A 27 A11 C 28 B12 B 29 C13 B 30 C14 C 31 D15 E (3π/2) 32 D16 C 33 A17 D 34