865 CHAPTER 8 Review Exercises Concepts Examples Graph x = 2 - sin t, y = cos t - 1, for 0 … t … 2p. −3.1 −5 3.1 5 Joe kicks a football from the ground at an angle of 45° with a velocity of 48 ft per sec. Give the parametric equations that model the path of the football and the distance it travels before hitting the ground. x = 148 cos 45°2t = 2422 t y = 148 sin 45°2t - 16t2 = 2422 t - 16t2 When the ball hits the ground, y = 0. 2422 t - 16t2 = 0 Substitute y = 0. 8t A322 - 2tB = 0 Factor. t = 0 or t = 322 2 Zero-factor property (Reject) The distance it travels is x = 2422 Q3 22 2 R = 72 ft. Parametric Equations of a Plane Curve A plane curve is a set of points 1x, y2 such that x = ƒ1t2, y = g1t2, and f and g are both defined on an interval I. The equations x =ƒ1t2 and y =g1t2 are parametric equations with parameter t. Flight of an Object If an object has initial velocity v and initial height h, and travels such that its initial angle of elevation is u, then its flight after t seconds can be modeled by the following parametric equations. x = 1v cos U2 t and y = 1v sin U2 t −16 t2 +h 8.8 Parametric Equations, Graphs, and Applications Chapter 8 Review Exercises Use the law of sines to find the indicated part of each triangle ABC. 1. Find b if C = 74.2°, c = 96.3 m, B = 39.5°. 2. Find B if A = 129.7°, a = 127 ft, b = 69.8 ft. 3. Find B if C = 51.3°, c = 68.3 m, b = 58.2 m. 4. Find b if a = 165 m, A = 100.2°, B = 25.0°. 5. Find A if B = 39° 50′, b = 268 m, a = 340 m. 6. Find A if C = 79° 20′, c = 97.4 mm, a = 75.3 mm. Answer each question. 7. If we are given a, A, and C in a triangle ABC, does the possibility of the ambiguous case exist? If not, explain why. 8. Can triangle ABC exist if a = 4.7, b = 2.3, and c = 7.0? If not, explain why. Answer this question without using trigonometry.
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