EXERCISES Practice and Problem Solving
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1 EXERCISES Practice and Problem Solving For more ractice, see Extra Practice. A Practice by Examle Examles 1 and (ages 71 and 71) Write each measure in. Exress the answer in terms of π and as a decimal rounded to the nearest hundredth Write each measure in degrees. Round your answer to the nearest degree, if necessary Examle (age 71) 1. Coy and comlete the diagram at the right. Fill in the missing measures in or degrees. The measure of an angle in standard osition is given. Find the exact values of cos and sin for each angle measure Examle (age 71) Use each circle to find the length of the indicated arc. Round your answer to the nearest tenth c. t m 9 ft cm 11 5 m. a. 5. m in. w z 5 11 cm Lesson 1- Radian Measure
2 Examle 5 (age 715) Find the length of each arc in. 1.5 ft B Aly Your Skills 8. Sace A geostationary satellite is ositioned 5,800 km above Earth s surface. It takes h to comlete one orbit. The radius of Earth is about 00 km. a. What distance does the satellite travel in 1 h? b. What distance does the satellite travel in h? c. What distance does the satellite travel in.5 h? d. What distance does the satellite travel in 5 h? e. Critical Thinking After how many hours has the satellite traveled 00,000 km? 9. Automobile Design Suose a windshield wier arm has a length of in. and rotates through an angle of What distance does the ti of the wier travel as it moves once across the windshield? 0. Geograhy The lines of longitude that aroximate the standard time zones are equally saced around the equator. a. Suose you use central angles to divide a circle into equal arcs. Exress the measure of each angle in degrees and in. b. The radius of the equator is about 90 mi. About how wide is each time zone at the equator? c. The radius of the Arctic Circle is about 1580 mi. About how wide is each time zone at the Arctic Circle? In which quadrant, or on which axis, does the terminal side of each angle lie? Draw an angle in standard osition with each given measure. Then find the values of the cosine and sine of the angle to the nearest hundredth Need Hel? Two triangles are congruent if their corresonding sides are congruent and their corresonding angles are congruent.. a. Geometry Draw a unit circle on the coordinate lane. Then draw five 9 angles in standard osition measuring 5, 5, 5, 5,and 10. b. For each angle, comlete a right triangle. Place the hyotenuse along the terminal side (from the origin to the unit circle). Place one leg along the x-axis. The other leg will be arallel to the y-axis. c. Critical Thinking Are the five triangles congruent? Justify your answer by using the values of sin u and cos u for each angle.. Oen-Ended Draw an angle in standard osition. Draw a circle with its center at the vertex of the angle. Find the measure of the angle in and degrees Chater 1 Periodic Functions and Trigonometry
3 5. Transortation Suose the radius of a bicycle wheel is 1 in. (measured to the outside of the tire). Find the number of through which a oint on the tire turns when the bicycle has moved forward a distance of 1 ft. 9. Error Analysis A student wanted to rewrite in degrees. The screen shows her 9* /*0/* calculation. What error did the student make? Find the length of each arc. Then find the measures of two angles coterminal with the given angle ft 5π 05 9 in. C Challenge 9. Writing Two angles are measured in. Exlain how to tell whether the angles are coterminal without rewriting their measures in degrees. 50. Music A CD with diameter 1 cm sins in a CD layer. Calculate how much farther a oint on the outside edge of the CD travels in one revolution than a oint 1 cm closer to the center of the CD. 51. Geograhy Assume that Earth is a shere with radius 90 miles. A town is at latitude 8 N. Find the distance in miles from the town to the North Pole. (Hint: Latitude is measured north and south from the equator.) The given angle is in standard osition. Find the radian measure of the angle that results after the given number of revolutions from the terminal side of. 5. u = ; 1 clockwise revolution 5. u = ; clockwise revolutions 5. u = ; 1 counterclockwise revolution 55. u = 5 ; 1 counterclockwise revolutions measure of central angle length of arc 5. Reasoning Use the roortion measure of one comlete rotation = circumference to derive the formula s = ru. Use u for the central angle measure and s for the arc length. Measure the rotation in. Lesson 1- Radian Measure
4 57. a. Use the cartoon below. Use a calculator to evaluate the first three terms of Jason s exression to seven decimal laces. Then evaluate the first four terms. Which is a better estimate of cos 08? b. Jason s exression will aroximate the cosine of any angle if you know its radian measure. Write a general form of his exression by substituting x for. c. Use the general formula you wrote in art (b) to estimate cos A10 B to the nearest thousandth. What is the angle measure, in degrees? Standardized Test Pre Multile Choice Take It to the NET Online lesson quiz at Web Code: aga-10 Short Resonse 58. Which airs of measurements reresent the same angle measures? I. 08, 7 II. 158, III. 1508, 5 A. I and II only B. I and III only C. II and III only D. I, II, and III 59. What is the exact value of cos A 5 B?! F.! G. H. - 1! I. 0. In a circle, an arc of length 8 cm is interceted by a central angle of. What is the radius of the circle? A. cm B. 1 cm C. 1 1 cm D. 1 cm 1. Two arcs have the same length. One arc is interceted by an angle of in a circle of radius 15 cm. If the radius of the other circle is 5 cm, what central angle intercets the arc? F. G. 9 H. I Describe the relationshi between a central angle of one radian and the radius of the circle Chater 1 Periodic Functions and Trigonometry
5 Mixed Review Lesson 1- Lesson 1- Lesson 10- Sketch each angle in standard osition Find the mean and the standard deviation for each set of values Write an equation of a circle with the given center and radius. 71. center (0, 0), radius 8 7. center (0, -5), radius 7. center (, 7), radius.5 7. center (-8, ), radius Lesson 1- Radian Measure
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