Chapter Review 467 41. Use a calculator to approximate π sin 8 . Round the answer to two decimal places. 42. Use a calculator to approximate sec ° 10 . Round the answer to two decimal places. 43. Determine the signs of the six trigonometric functions of an angle θ whose terminal side is in quadrant III. 44. Name the quadrant θ lies in if θ > cos 0 and θ < tan 0. 45. Find the exact values of the six trigonometric functions of t if = − ⎛ ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟ ⎟ P 1 3 , 2 2 3 is the point on the unit circle that corresponds to t. 46. Find the exact value of sin t, cos t, and tan t if ( ) = − P 2, 5 is the point on a circle that corresponds to t. 47. What are the domain and the range of the secant function? What is the period? 48. (a) Convert the angle ° ′ ″ 32 2035 to a decimal in degrees. Round the answer to two decimal places. (b) Convert the angle ° 63.18 to ° ′ ″ D M S form. Express the answer to the nearest second. 49. Find the length of the arc subtended by a central angle of ° 30 on a circle of radius 2 feet. What is the area of the sector? 50. The minute hand of a clock is 8 inches long. How far does the tip of the minute hand move in 30 minutes? How far does it move in 20 minutes? 51. Angular Speed of a Race Car A race car is driven around a circular track at a constant speed of 180 miles per hour. If the diameter of the track is 1 2 mile, what is the angular speed of the car? Express your answer in revolutions per hour (which is equivalent to laps per hour). 52. Lighthouse Beacons The Montauk Point Lighthouse on Long Island has dual beams (two light sources opposite each other). Ships at sea observe a blinking light every 5 seconds. What rotation speed is required to achieve this? 53. Alternating Current The current I, in amperes, flowing through an AC (alternating current) circuit at time t is π π ( ) ( ) = + ≥ I t t t 220sin 30 6 0 (a) What is the period? (b) What is the amplitude? (c) What is the phase shift? (d) Graph this function over two periods. 54. Monthly Temperature The given data represent the average monthly temperatures for Phoenix, Arizona. (a) Draw a scatter plot of the data for one period. (b) Find a sinusoidal function of the form ω φ ( ) = − + y A x B sin that models the data. (c) Draw the sinusoidal function found in part (b) on the scatter plot. (d) Use a graphing utility to find the sinusoidal function of best fit. (e) Graph the sinusoidal function of best fit on the scatter plot. January, 1 Month, x Average Monthly Temperature, 8F February, 2 March, 3 April, 4 May, 5 June, 6 July, 7 August, 8 September, 9 October, 10 November, 11 December, 12 56 60 65 73 82 91 95 94 88 77 64 55 Source: U.S. National Oceanic & Atmospheric Administration 55. Unit Circle On the given unit circle, fill in the missing angles θ π ( ) ≤ ≤ 0 2 and the corresponding points P. x y P P P P P P P P P P P Angle: P Angle: P Angle: P Angle: Angle: Angle: Angle: Angle: Angle: Angle: Angle: Angle: Angle: Angle: Angle: Angle: P P p— 6 p— 4 p— 3 11p ——6 5p ——3 7p ——4
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