872 CHAPTER 8 Applications of Trigonometry 15. Height of a Tree A tree leans at an angle of 8.0° from the vertical, as shown in the figure. From a point 8.0 m from the bottom of the tree, the angle of elevation to the top of the tree is 66°. Find the slanted height x in the figure. 16. Bearing and Airspeed Find the bearing and airspeed required for a plane to fly 630 mi due north in 3.0 hr if the wind is blowing from a direction of 318° at 15 mph. Find the bearing to the nearest degree and the airspeed to the nearest 10 mph. 17. Incline Angle A force of 16.0 lb is required to hold a 50.0-lb wheelbarrow on an incline. What angle does the incline make with the horizontal? 18. Magnitude of a Force Two forces of 135 newtons and 260 newtons act on a point, forming an angle of 115°. Find the magnitude of the resultant force. 19. For the complex numbers w = 2 - 4i and z = 5 + i, find w + z in rectangular form and give a geometric representation of the sum. 20. Write each complex number in trigonometric (polar) form, where 0° … u 6360°. (a) 3i (b) 1 + 2i (c) -1 - i23 21. Write each complex number in rectangular form. (a) 31cos 30° + i sin 30°2 (b) 4 cis 40° (c) 31cos 90° +i sin 90°2 22. For the complex numbers w = 81cos 40° + i sin 40°2 and z = 21cos 10° + i sin 10°2, find each of the following in the form specified. (a) wz (trigonometric form) (b) w z (rectangular form) (c) z3 (rectangular form) 23. Find the four complex fourth roots of -16i. Write answers in trigonometric form. 24. Convert the given rectangular coordinates to polar coordinates. Give two pairs of polar coordinates for each point. (a) 10, 52 (b) 1-2, -22 25. Convert the given polar coordinates to rectangular coordinates. (a) 13, 315°2 (b) 1-4, 90°2 8.08 668 x 8.0 m Identify and graph each polar equation for u in 30°, 360°2. 26. r = 1 - cos u 27. r = 3 cos 3u 28. Convert each polar equation to a rectangular equation, and sketch its graph. (a) r = 4 2 sin u - cos u (b) r = 6 Graph each pair of parametric equations. 29. x = 4t - 3, y = t2, for t in 3-3, 44 30. x =2 cos 2t, y =2 sin 2t, for t in 30, 2p4
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