590 CHAPTER 5 Trigonometric Functions 69. Distance between Two Points Two cars leave an intersection at the same time. One heads due south at 55 mph. The other travels due west. After 2 hr, the bearing of the car headed west from the car headed south is 324°. How far apart are they at that time? 70. (Modeling) Height of a Satellite Artificial satellites that orbit Earth often use VHF signals to communicate with the ground. VHF signals travel in straight lines. The height h of the satellite above Earth and the time T that the satellite can communicate with a fixed location on the ground are related by the model h = R ¢ 1 cos 180T P - 1≤, where R = 3955 mi is the radius of Earth and P is the period for the satellite to orbit Earth. (Data from Schlosser, W., T. Schmidt-Kaler, and E. Milone, Challenges of Astronomy, Springer-Verlag.) (a) Find h to the nearest mile when T = 25 min and P = 140 min. (Evaluate the cosine function in degree mode.) (b) What is the value of h to the nearest mile if T is increased to 30 min? 1. Give the measures of the complement and the supplement of an angle measuring 67°. Perform each conversion. 4. 74° 18′ 36″ to decimal degrees 5. 45.2025° to degrees, minutes, seconds Find the measure of each marked angle. 2. (7x + 19)° (2x – 1)° 3. (–8x + 30)° (–3x + 5)° Solve each problem. 6. Find the angle of least positive measure that is coterminal with each angle. (a) 390° (b) -80° (c) 810° 7. Rotating Tire A tire rotates 450 times per min. Through how many degrees does a point on the edge of the tire move in 1 sec? Sketch an angle u in standard position such that u has the least positive measure, and the given point is on the terminal side of u. Then find the values of the six trigonometric functions for the angle. Rationalize denominators when applicable. If any of these are undefined, say so. 8. 12, -72 9. 10, -22 Work each problem. 10. Draw a sketch of an angle in standard position having the line with the equation 3x - 4y = 0, x … 0, as its terminal side. Indicate the angle of least positive measure u, and find the values of the six trigonometric functions of u. Chapter 5 Test
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