1. Use a calculator to find to the nearest tenth of a degree, if 0 < < 360 and
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1 Practice Test 2 Numeric Response 1. Use a calculator to find to the nearest tenth of a degree, if 0 < < 360 and with in QIII 2. Use a calculator to find to the nearest tenth of a degree, if 0 < < 360 and with in QIII 3. Find, if 0 < < 360 and and in QIII 4. Find, if and and in QIII 5. Find the radian measure of angle, if is a central angle in a circle of radius r, and cuts off an arc of length s. r = 2 inches, s = 6 inches radians 6. For the problem below, is a central angle in a circle of radius r. Find the length of arc s cut off by. inches. s = inches 7. If the distance to the sun is approximately 93 million miles, and, from the earth, the sun subtends an angle of approximately, estimate the diameter of the sun to the nearest 10,000 miles. miles
2 8. The figure is a model of George Ferris's Ferris wheel. The diameter of the wheel is 246 feet; and is the central angle formed as a rider travels from his or her initial position to position. Find the distance traveled by the rider if. Round your answer to the nearest tenth. s = ft 9. is a central angle that cuts off an arc of length s. Find the radius of the circle if cm. r = cm 10. is a central angle that cuts off an arc of length s. Find the radius of the circle if m. r = m 11. Find the linear velocity of a point moving with uniform circular motion, if the point covers a distance s in an amount of time t, where s = 18 cm and t = 2 sec cm/sec 12. Find the distance s covered by a point moving with linear velocity v for a time t if v = 24 mi/hr and t = 15 min mi 13. Point P sweeps out central angle as it rotates on a circle of radius r. Find the angular velocity of point P. rad/min
3 14. Point P moves with angular velocity on a circle of radius r. Find the distance s traveled by the point in time t. ft 15. The figure below is a model of the Ferris wheel. The diameter of the wheel is 171 feet, and one complete revolution takes 15 minutes. Find the linear velocity of a person riding on the wheel. Give your answer in miles per hour and round to the nearest hundredth. mph 16. Use a calculator to evaluate the expression to the nearest tenth of a degree, if necessary. 17. Use your graphing calculator to graph in degree mode. Use the graph with the appropriate command to evaluate the expression. 18. Through how many radians does the minute hand of a clock turn during a 5-minute period? 19. For the following expression, find the value of y that corresponds to each value of x, then write your results as ordered pairs (x, y). for
4 20. Two cities are approximately 550 miles apart on the surface of the earth. Assuming that the radius of the earth is 4,000 miles, find the radian measure of the central angle with its vertex at the center of the earth that has one city on one side and another one on the other side. radians 21. Graph the unit circle using parametric equations with your calculator set to radian mode. Use a scale of. Trace the circle to find all values of t between 0 and satisfying the following statement. Round your answers to the nearest ten-thousandth. t = 22. For the problem below, is a central angle in a circle of radius r. Find the length of arc s cut off by. inches. s = inches 23. Arc length The minute hand of a clock is 1.2 centimeters long. How far does the tip of the minute hand travel in 30 minutes? centimeters 24. The pendulum on a grandfather clock swings from side to side once every second. If the length of the pendulum is 4 feet and the angle through which it swings is how far does the tip of the pendulum travel in 1 second? feet
5 25. is a central angle that cuts off an arc of length s. Find the radius of the circle if km. r = km 26. Point P sweeps out central angle as it rotates on a circle of radius r. Find the angular velocity of point P. rad/sec 27. Point P moves with angular velocity on a circle of radius r. Find the distance s traveled by the point in time t. m 28. Find the angular velocity associated with the given rpm. 9.6 rpm rad/min 29. A wheel with radius r rotates at 13 rpm. Find v if r = 5 ft ft/min 30. A cable railway had a 14-foot-diameter pulley to drive the cable (see the figure). In order to keep the cable cars moving at a linear velocity of 13 miles per hour, how fast would the pulley need to turn (in revolutions per minute)? (1 mi = 5,280 ft) rpm 31. A woman rides a bicycle for 2 hours and travels 26 kilometers (about 16 miles). Find the angular velocity of the wheel if the radius is 30 centimeters. rad/min
6 32. The graph below is one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is correct. 33. The graph below is one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is correct. 34. The graph below is one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is correct.
7 35. The graph below is one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is correct. 36. The graph below is one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is correct. 37. The graph below is one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is correct.
8 38. Evaluate the expression without using a calculator, and write your answer in radians. 39. Evaluate the expression without using a calculator, and write your answer in radians. 40. Evaluate the expression without using a calculator, and write your answer in radians. 41. Simplify if for some real number. 42. Evaluate without using a calculator. 43. Evaluate without using a calculator. 44. Evaluate without using a calculator. 45. Evaluate without using a calculator. 46. Simplify if. 47. Simplify if
9 48. Without using your calculator, graph one cycle of the equation y = sin(x + π/3). Find the amplitude, phase shift, vertical translation and period. 49. Without using your calculator, graph one cycle of the equation y = -2sec(3x + π/2). Find the amplitude, phase shift, vertical translation and period. 50. Without using your calculator, graph one cycle of the equation y = 1 + 3tan(x + π/6). Find the amplitude, phase shift, vertical translation and period.
10 Practice Test 2: This packet must be complete in order to earn 2pts extra credit Answer Section NUMERIC RESPONSE 1. ANS: ANS: ANS: ANS: ANS: 3 6. ANS: ANS: 810, ANS: ANS: ANS: ANS: ANS: ANS: ANS: 7, ANS: 0.41 MSC: mctr MSC: mctr MSC: mctr MSC: mctr MSC: mctr MSC: mctr MSC: mctr MSC: mctr MSC: mctr MSC: mctr MSC: mctr MSC: mctr MSC: mctr MSC: mctr
11 16. ANS: ANS: 45 MSC: mctr MSC: mctr MSC: mctr SHORT ANSWER 18. ANS: 19. ANS: MSC: mctr ANS: MSC: mctr ANS: MSC: mctr ANS: MSC: mctr ANS: MSC: mctr ANS: MSC: mctr ANS: MSC: mctr ANS: MSC: mctr
12 27. ANS: MSC: mctr ANS: MSC: mctr ANS: MSC: mctr ANS: MSC: mctr ANS: MSC: mctr ANS: MSC: mctr ANS: MSC: mctr ANS: MSC: mctr ANS: MSC: mctr ANS: MSC: mctr ANS: MSC: mctr ANS: MSC: mctr
13 39. ANS: MSC: mctr ANS: MSC: mctr ANS: MSC: mctr ANS: MSC: mctr ANS: MSC: mctr ANS: MSC: mctr ANS: MSC: mctr ANS: x 47. ANS: MSC: mctr MSC: mctr MSC: mctr
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