MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
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1 Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the angle to decimal degrees and round to the nearest hundredth of a degree. 1) ) A) 6.31 B) 6.5 C) 65.5 D) 6.6 Convert the angle to degrees, minutes, and seconds. ) ) A) B) C) D) Convert from degrees to radians. Use the value of found on a calculator and round answers to four decimal places, as needed. 3) 36 3) A) 5 B) C) 7 D) 6 Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two decimal places. ) / ) A) ( /) B) 90 C) 90 D) 1.57 Use the arc length formula and the given information to find the indicated quantity. 5) r = 6 in., = rad; find s 5) A) 1 3 in. B) 3 in. C) in. D) 1 in. Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. 6) 6) Find sin A and cos A. A) sin A = 5 ; cos A = 5 3 B) sin A = 3 ; cos A = 3 C) sin A = 3 5 ; cos A = 5 D) sin A = 5 ; cos A = 3 5 1
2 Assume that is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function. 7) sin = 9 ; cos 7) 10 A) B) C) 10 9 D) 19 9 Solve for x. Round your answer to decimal places. 8) 8) 10 x 37 A) 6.0 B) 7.99 C) 16.6 D) 1.5 Solve the right triangle for all missing sides and angles to the nearest tenth. 9) 9) c = 19 B = 16 A) A = 7, a = 5., b = 5. B) A = 7, a = 18.3, b = 5. C) A = 7, a = 5., b = 18.3 D) A = 7, a = 18.3, b = 5. Solve the problem. 10) From a distance of 50 feet from the base of a building, the angle of elevation to the top of the building is 68. Estimate the height of the building to the nearest foot. A) 19 feet B) 1 feet C) 6 feet D) 0 feet 10) Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. 11) 7 11) A) 07 ; -153 B) 387 ; -333 C) 387 ; -153 D) 117 ; -63
3 Find the trigonometric function value for the angle shown. 1) cos 1) A) cos = 33 7 B) cos = 7 C) cos = 7 D) cos = 33 Suppose that is in standard position and the given point is on the terminal side of. Give the exact value of the indicated trig function for. 13) (18, ); find sin. 13) A) 5 B) 3 C) 3 5 D) 3 Determine whether the given function is positive or negative for values of t in the specified quadrant. 1) Quadrant II, cos t 1) A) Positive B) Negative Choose the point on the terminal side of. 15) = -5 15) A) (-1, 3) B) (- 3, 1) C) (-1, 1) D) ( 3, -1) Evaluate the trigonometric function of the given quadrantal angle. 16) sin ) A) 0 B) -1 C) 1 D) Undefined Evaluate without using a calculator. 17) sin, if cos = 9 and tan < 0 17) A) - 65 B) - 65 C) - 9 D) Find the value of the unique real number between 0 and that satisfies the given conditions. 3 18) sin = and tan > 0 18) A) 3 B) 6 C) 3 D) 3
4 Find the amplitude of the function. 19) y = 1.5 sin 8x 19) A) 8 B) 3 C) 1.5 D) 8 Find the period of the function. 0) y =.5 sin x 0) A).5 B) C) D) Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). 1) f(x) = - cos 5x ; g(x) = cos x 1) A) Horizontal shrink by a factor 1, vertical stretch by a factor of, reflection across x-axis 5 B) Horizontal shrink by a factor 1, vertical stretch by a factor of, reflection across y-axis 5 C) Horizontal shrink by a factor 1, vertical stretch by a factor of 5, reflection across y-axis D) Horizontal stretch by a factor 5, vertical stretch by a factor of, reflection across x-axis Graph the function.
5 ) y = sin 1 x ) A) B) C) D) Identify the maximum and minimum values of the function. 3) y = 3 cos x 3) A) Maximum value = 3; minimum value = 0 B) Maximum value = 3; minimum value = -3 C) Maximum value = 6; minimum value = -6 D) Maximum value = 3 ; minimum value = - 3 5
6 Find the zeros of the function in the interval [-, ]. ) f(x) = 3 cos x ) A) 0, ±, ± B) ±, ± 3 C) 0, ±, ± 3 D) ±, ±, ± 3, ± Write an equation for a sine curve that has the given amplitude and period, and which passes through the given point. 5) Amplitude 5, period, point (0, 0) 5) A) y = 5 sin x B) y = 5 sin x C) y = 5 sin x D) y = 5 sin x Match the function with its graph. 6) 1) y = tan x ) y = cot x 3) y = -tan x ) y = -cot x 6) A) B) C) D) A) 1C, A, 3B, D B) 1A, D, 3C, B C) 1A, B, 3C, D D) 1B, D, 3C, A 6
7 Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph. 7) y = -tan 1 8 x + 6 7) A) Reflection across the x-axis, horizontal shrink by a factor of 1, and vertical translation down 8 6 units. B) Reflection across the x-axis, horizontal stretch by a factor of 8, and vertical translation up 6 units. C) Reflection across the x-axis, horizontal translation to the right 8 units, and vertical translation up 6 units. D) Horizontal stretch by a factor of 8 and a vertical translation up 6 units. Solve for x in the given interval. 8) sec x = -, x 3 8) A) 7 6 B) 3 C) 3 D) 5 Find the exact value of the real number y. 9) y = sin-1 3 9) A) 3 B) 3 C) D) 3 Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. 30) sin-1 (0.56) 30) A) B) 3.33 C) D) 9. Use a calculator to find the approximate value of the expression. Express your answer in radians and round to three decimal places. 31) sin-1 ( ) 31) A) 3.75 B) C) D) 1.70 Find the exact value of the composition. 3) sin (arctan ()) 3) A) 5 5 B) 5 C) 5 D) 5 Find the exact solution to the equation without a calculator. 33) sin (sin-1 x) = ) A) 0.6 B) 0 C) 0.3 D) 1. Solve the problem. 3) From a boat on the lake, the angle of elevation to the top of a cliff is 7'. If the base of the cliff is 1751 feet from the boat, how high is the cliff (to the nearest foot)? A) 811 ft B) 818 ft C) 808 ft D) 81 ft 3) 7
8 35) A person is watching a car from the top of a building. The car is traveling on a straight road directly toward the building. When first noticed the angle of depression to the car is 10. When the car stops, the angle of depression is The building is 70 feet tall. How far did the car travel from when it was first noticed until it stopped? Round your answer to the hundredths place. A) ft B) ft C) ft D) ft 35) 8
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