Pre-Calc Chapter Sample Test 1. Determine the quadrant in which the angle lies. (The angle measure is given in radians.) π 8 I B) II C) III D) IV E) The angle lies on a coordinate axis.. Sketch the angle in standard position 11π/1 B) C) D) E) none of these. Determine two coterminal angles (one positive and one negative) for the given angle. Give your answer in radians: π/ 9π/, -7π/. Find (if possible) the complement and supplement of the given angle: 1. B) C) D) E) 5. Convert the angle measure to decimal degree form: 115 6' 11.567 B) 115.06 C) 115. D).008 E) 6590.50
Page 6. Convert the angle measure to DMS form: 10.65 10 7' B) 10 7' 1" C) 10 65' D) 10 1' 7" E) 10 1' 7. Find the angle in radians. B) C) D) E) 8. Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. radius: r = 9 centimeters arc length: s = centimeters 9 B) 9 π C) π D) E) 9 18 9 9. Find the length of the arc on a circle of radius r intercepted by a central angle θ. 7π radius: r = 11 meters central arc: θ = 7 π meters B) 77 π meters C) 87 π meters D) 77 π meters E) 77 meters 8 10. Find the area of the sector of the circle with radius r and central angle θ. radius: r = 5 miles π central arc: θ = π 10π square miles D) square miles B) 5π 10 square miles E) square miles C) 50π square miles
Page 11. Determine the exact value of tanθ. θ 7, 5 5 7 B) 7 C) D) 7 7 E) 5 7 1. Find the point (x, y) on the unit circle that corresponds to the real number t: B) C) D) E) 1. Evaluate the trigonometric function using its period as an aid. 5π cos 1 B) 1 C) D) E)
Page 1. Use the figure and a straightedge to approximate the value of cos.5 1.00 B) 0.11 C) 0.99 D) 0.11 E) 1.01 15. Find the exact value of the given trigonometric function of the angle θ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.) Find: cscθ c a B) C) D) 1 E) θ a a = 16. Given that cosθ =, find cscθ. 7 [Hint: Sketch a right triangle corresponding to the trigonometric function of the acute angle θ, then use the Pythagorean Theorem to determine the third side.] B) 7 7 C) D) 8 E) 7 17. Use the given function values and the trigonometric identities (including the cofunction identities), to find the indicated trigonometric function. csc θ =,cosθ = ; find sin ( 90 θ ) 5 5 B) 5 C) 5 D) 68 E) 18. Use a calculator to evaluate the function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.) sec 7.7 1.195 B) 0.670 C) 1.859 D) 0.98 E) 1.0990
Page 5 19. Solve for r. r 1 r = B) 1 r = C) r = 1 5 1 D) r = E) r = 1 0. The point(,)is on the terminal side of an angle in standard position. Determine the exact value of tanθ. B) C) D) E) fracnum(q, p) / fracden(q, p) fracnum(q, cafac) fracsign(q,cafac) leadcoeff(fracden(q,cafac)) carad fracden(q, p) fracsign(q, p) fracnum(q, p) fracnum(q, p+ q) fracsign(q, p+ q) fracden(q, p+ q) fracnum(q, dafac) fracsign(q,dafac) leadcoeff(fracden(q,dafac)) darad 1. State the quadrant in which θ lies: cot( θ ) < 0 and sec( θ ) < 0 Quadrant IV D) Quadrant I B) Quadrant III E) Quadrant II or Quadrant IV C) Quadrant II. Use the function value and constraint below to evaluate the given trigonometric function. Function Value Constraint Evaluate: sec θ = tanθ < 0 cotθ 15 B) 15 C) 1 1 D) E) undefined 15. Find the reference angle θ for the given angle θ : θ = 06 1 B) 6 C) 6 D) 5 E). Find the indicated trigonometric value in the specified quadrant. Function Quadrant Trigonometric Value 1 cscθ = 9 III tanθ 9 B) 1 9 C) D) 1 1 E) undefined
Page 6 x π 5. Determine the period and amplitude of y = cos + 11 8. period: π π ; amplitude: D) period: ; amplitude: 11 11 π B) period: π ; amplitude: E) period: ; amplitude: 11 C) period: 11π ; amplitude: 8 6. Describe the relationship between f ( x) = cos( x) and gx ( ) = cos x 5. Consider amplitude, period, and shifts. The period of g(x) is three times shorter than the period of f(x). Graph of g(x) is shifted downward 5 unit(s) relative to the graph of f(x). B) The amplitude of g(x) is three times the amplitude of f(x). Graph of g(x) is shifted downward 5 unit(s) relative to the graph of f(x). C) The period of g(x) is three times the period of f(x). Graph of g(x) is shifted upward 5 unit(s) relative to the graph of f(x). D) The amplitude of g(x) is three times the amplitude of f(x). Graph of g(x) is shifted upward 5 unit(s) relative to the graph of f(x). E) The period of g(x) is five times the period of f(x). Graph of g(x) is shifted downward unit(s) relative to the graph of f(x). 7. Find a and d for the function f ( x) = asin x+ d such that the graph of f ( x ) matches the graph below. a = ; d = -1 B) a = ; d = 1 C) a = -; d = 1 D) a = ; d = E) a = ; d = - 8. Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.) cot π 0.018 B) 1.71 C) 0.9998 D) 0.577 E) 0.8660
Page 7 9. Given the graph of f(x) below, sketch the graph of:. B) C) D) E)
Page 8 0. Sketch the graph of the function below, being sure to include at least two full periods: B) C) D) E)
Version Page 9 1. Use a calculator to evaluate the function. Round your answers to four decimal places: csc8 8' 0.17 B) 1. C) 6.7919 D) 1.011 E) 1.081. Find a and d for the function f ( x) = asinx+ d such that the graph of f ( x ) matches the graph below. B) C) D) E). Use the properties of inverse trigonometric functions to evaluate sin arcsin ( 0.6) 0.9 B) 0. C) 0.76 D) 0. E) 0.6. x Write an algebraic expression that is equivalent to sin arctan 9. 9 x + 81 B) 9 C) x x + 81 x D) x + 81 9 E) x x + 81. 5. Find the altitude of the isosceles triangle shown below if θ = 0 and b = 5 centimeters. Round answer to two decimal places. θ θ.89 centimeters B) 0.67 centimeters C) 1.5 centimeters D) 1. centimeters E). centimeters b 6. A sign next to the highway at the top of Saura Mountain states that, for the next 6 miles, the grade is 11%. Determine the change in elevation (in feet) over the 6 miles for a vehicle descending the mountain. Round answer to nearest foot. 6 feet B) 85 feet C) 7 feet D) 978 feet E) 6 feet 7. Use a graphing utility to graph the damping factor and the function in the same viewing window. Describe the behavior of the function as x increases without bound.
Version Page 10 B) C) D) E) 8. Two lifeguards, Tony and Sharon, are kilometers apart and Tony is directly due south of Sharon on the beach. A stranded boat offshore is spotted by both lifeguards, and the bearings from Tony and Sharon, respectively, are N 1 E and S 1 E. Determine the distance the stranded boat is from the beach. Round answer to nearest tenth of a kilometer.. kilometers B). kilometers C).5 kilometers D) 5. kilometers E) 6. kilometers 9. While traveling across the flat terrain of Nevada, you notice a mountain directly in front of you. You calculate that the angle of elevation to the peak is.5, and after you drive 5 miles closer to the mountain it is 7. Approximate the height of the mountain peak above your position. Round your answer to the nearest foot. 55 feet B) 58 feet C) 5787 feet D) 6569 feet E) 8 feet
Version Page 11 0. A land developer wants to find the distance across a small lake in the middle of his proposed development. The bearing from A to B is N W. The developer leaves point A and travels 5 meters perpendicular to AB to point C. The bearing from C to point B is N 57 W. Determine the distance, AB, across the small lake. Round distance to nearest meter. B 9 meters B) 101 meters C) 119 meters D) 1 meters E) 19 meters A C Answer Key 1. C. B. E. E 5. D 6. A 7. D 8. B 9. C 0. C