untitled 1. Unless otherwise directed, answers to this question may be left in terms of π.

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1 Name: ate:. Unless otherwise directed, answers to this question may be left in terms of π. a) Express in degrees an angle of π radians. b) Express in radians an angle of 660. c) rod, pivoted at one end, rotates through π radians. If the rod is 6 inches long, how many inches does the free end travel? 4. Express sin 80 as a function of a positive acute angle in terms of sin x. sin 80. sin 80. sin 0 sin 0 d) wheel rotates at the rate of 65 revolutions per minute. Express in radians the angle through which it rotates in one second. 5. Write an expression to represent any angle coterminal with the angle 70 (n is an integer) n(60 ) n(60 ) n(80 ) n(40 ). If cot θ > 0, then the terminal side of θ may lie in what quadrant(s)? I and II. I and III. II only II and IV 6. Express cos( 50 ) as a function of a positive acute angle in terms of cos x. cos 50. cos 40. cos 50 cos 40. In which quadrant does the terminal ray of a standard position angle of 7 π radians lie? I. II. III there is no terminal ray 7. If both sin x and cos x decrease when x is increased, then x is in quadrant. one. two. three four page

2 8. If sin = and sec is negative, evaluate tan. Find the numerical value of tan π Those angles in standard position which may be denoted by π 4 + nπ, where n is an integer, form a set of coterminal angles. Write the number of the quadrant in which all angles of the set terminate. 4. Express tan(π ) in terms of tan 0. If the point P(, ) is a point on the terminal side of angle θ in standard position, then what is the exact value of sec θ? 5. What is the period of the function y = sin θ? 4π.. π. What is the reference angle for (60 θ) if 0 θ < 90? 6. What is the period of the function f (x) = sin π x?. π. 4 4π (. etermine the exact value of sin π ) etermine the the period of the function y = tan 7x... π 7. π. π 6π page

3 8. If y = f (x) has a period of 6, then y = f (x) has a period of For y = cos 6(θ ) state the () amplitude, () period, () vertical shift (positive or negative), and (4) phase displacement. () 8, () π 6, () 7, (4) 6. () 8, () π 6, () 7, (4) 6. () 7, () π 6, () 7, (4) () 8, () π 6, () 6, (4) 7 9. s x increases from 0 to π radians, sin x: increases throughout the interval. decreases throughout the interval. increases, then decreases decreases, then increases 0. For what value of k is the period of the function y = sin kx equal to 0?. The graph of f (x) is a cosine curve having a period of 0., amplitude of 8, phase displacement (for the cosine) of 0.0, and vertical displacement of 5. Which of the following is the equation of this graph? f (x) = 8 cos 0(x 0.0) 5. f (x) = 8 cos(0x 0.0) 5. f (x) = 8 cos 0(x 0.0) 5 f (x) = 8 cos 0π(x 0.0) 5. What is the amplitude of the function y = π sin 4x? π. π. 4 4π page

4 4. What is an equation for the graph shown? 6. The rotation of a Ferris wheel is modelled by the equation (t 0) h = 8 cos π where h is the height above ground. Suppose you get on at t = 0 at the bottom. How high will you be after s?.4 m. 8. m ( y = 8 cos x π ) m m. ( y = 4 cos x π ) + 8. ( y = 4 cos x π ) ( y = 8 cos x π ) What is the equation, in terms of cosine, of the graph? 5. Which of the following equations describes the graph? y = sin θ. y = sin θ. y = sin θ y = sin θ page 4

5 8. Given the graph of this trigonometric function, over which domain(s) could an inverse function be constructed? 0. Express as an inverse function the value of x for which cos x = 0. arccos 4. arccos 4. arccos arccos I. II. III. [ π 4, π 4 [ π 4, 5π 4 [ 0, 5π 4 ] ] ]. Find the positive value of cos ( sin 5 ) I only. I and II. II and III I, II and III. Find the positive value of sin ( arctan ) Given the graph for f (x) = cos x, over which domain could f (x) be constructed?. If cos x = 0.8, what is the positive value of cos x in simplest form? ( π 4, π ) 4.. [π, π ] ( π 4, 9π ) 4 [ ] π, π 4. If tan α = 5 and cos α < 0, find cos α page 5

6 5. ship s pilot sights an 85 ft lighthouse at the top of a cliff whose base is 00 ft from the ship. The cliff is 75 ft high. What is the angle of elevation from the ship to the top of the lighthouse? 7. What is the equation for the graph shown? arctan 7 5. arctan 5. arctan arctan 7 5 arctan 7 60 y = cos x. y = csc x. y = cot x y = tan x 6. What is the equation for the graph shown? 8. Find the positive value of ( ) sin arctan 5 y = sin x. y = cos x 9. Simplify: sec cot + tan. y = tan x y = csc x cos. sin cos. sin tan page 6

7 40. Simplify: cos θ sin θ sec θ + tan θ. sec θ + cot θ. csc θ + cot θ sec θ + csc θ 44. For what values of is the following statement true? sin + cos = no real values of. all real values of. some but not all real values of = π only 4. Simplify the expression: csc csc sin csc. sec. sec cot Simplify: + sin θ + sin θ 0. csc θ. sec θ sin θ cos θ Which of the following statements is true for the given diagram? cos θ + sin θ = 5k. k cos θ + k sin θ = 5. k cos θ + k sin θ = 5 4. Express in terms of sec θ: k (cos θ + sin θ) = 5 tan θ sin θ sin θ sec θ sec θ +. sec θ sec θ +. sec θ sec θ + sec 4 θ sec θ Prove: sec θ + sin θ = sec θ sec θ tan θ cos θ page 7

8 ( π 47. cos π ) can be expanded to: 4 5. Write as a single trigonometric function: cos 4 sin 4 sin π 4 sin π 4 cos π cos π 4. cos π cos π 4 sin π sin π 4 sin 86. sin 86. cos 86 cos 86 sin 56. cos π cos π 4 + sin π sin π 4 sin π cos π 4 cos π sin π If sin θ = t, express cos(90 + θ) in terms of t. t. t. t t 5. If sin =, cos = 4, is in quadrant II, and is in quadrant IV, evaluate sin( + ). (nswer in radical form and put everything over a common denominator.) The expression sin(45 + x) is always equal to:. + sin x. cos x sin x cos x cos x + sin x 5. Find the area of a triangle whose sides are 5, 6 and ( π ) ( π ) 50. sin 4 + x + sin 4 x is equivalent to: sin π 4. sin x. cos x + sin x 54. The area of is 4 cm. m = 4 and = 7 cm. To decimal place, how long is? page 8

9 55. What is the area of a parallelogram that has adjacent sides of cm and 5 cm, and an angle of 75? nswer to decimal place. 58. In triangle, the measure of angle is twice the measure of angle Which of the following is equivalent to a b cos.. cos sin 56. For quadrilateral RK, K = 55, KR = 5, = R = x, and K = y. 59. What is the exact value of cos QPR? a) Find the area of each triangle in terms of x and y. b) What is the area of RK? Use trigonometric identities and put your answer in simplest form. 60. In triangle, = 8 cm, = 5 cm, and m = 0. Exactly how long is? Given triangle with a = 7, and b = 8, which of the following gives the cosine of angle in terms of the opposite side c? c. c. 4c c 6. In, = 0, = 05 and b = 6. Find a.. 6. page 9

10 6. For triangle MNO, m = 4, n = 7 and O = 60, what is the length of o in radical form? 6. If the data = 6, b = 6 and c = 0 are used, triangle : must be a right triangle. must be an acute triangle. must be an obtuse triangle may be either an acute triangle or an obtuse triangle page 0

11 Problem-ttic format version c 0 06 Educide Software Licensed for use by dpehrman@atlanta.k.ga.us Terms of Use at 09/6/ ; π; 4π; 5 π F.TF. 5. F.TF.4. F.TF. 6. F.TF.4. F.TF. 7. F.TF F.TF. F.TF. F.TF. F.TF F.TF IV F.TF. F.TF. θ F.TF. F.TF. F.TF. tan F.TF F.TF.4 F.TF.4 0. F.TF y = 5 + cos π (x 0) 0

12 Teacher s Key Page F.TF.6 F.TF [proof] F.TF.9 F.TF.9 F.TF.9 F.TF.9 F.TF.9 F.TF.9 G.SRT.9 4. cm G.SRT cm G.SRT K = xy sin 55, KR = xy sin 5 ; RK = xy(sin 45 cos 0) G.SRT G.SRT.0 G.SRT.0

13 Teacher s Key Page G.SRT.0 G.SRT. G.SRT. G.SRT. G.SRT.