Concept explainers
Finding Cartesian from Parametric Equations
Exercises 1−18 give parametric equations and parameter intervals for the motion of a particle in the xy-plane. Identify the particle’s path by finding a Cartesian equation for it. Graph the Cartesian equation. (The graphs will vary with the equation used.) Indicate the portion of the graph traced by the particle and the direction of motion.
x = -sec t, y = tan t, -p/2 < t < p/2
Learn your wayIncludes step-by-step video
Chapter 10 Solutions
University Calculus: Early Transcendentals (4th Edition)
Additional Math Textbook Solutions
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (2nd Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Precalculus (10th Edition)
Calculus & Its Applications (14th Edition)
- Shooting into the Wind Suppose that a projectile is fired into a headwind that pushes it back so as to reduce its horizontal speed by a constant amount . Find parametric equations for the path of the projectile.arrow_forwardFind a set of parametric equations to represent the graph of y=x2+2, using each parameter. a. t=x b. t=2xarrow_forwardFind the rectangular equation of the curve given by the parametric equations below. Then graph the curve and show its orientation. Assume that t can be any real number. x=7, Explanatis 1 y=-t 2 Rectangular equation: -8 -6 -4 -2 1-2- 2 4 6 8 X X 00 0=0arrow_forward
- Construct parametric equations describing the graph of the line passing through the following points. (-7, – 7) and (8, – 14) If y = 1+t, find the parametric equation for x.arrow_forwardA pair of parametric equations is given. x = 2t, y = t + 4 (a) Sketch the curve represented by the parametric equations. Use arrows to indicate the direction of the curve as t increases.arrow_forwardFind the rectangular equation of the line given by the parametric equations below. Then graph the line and show its orientation. Assume that t can be any real number. x=-t+3 y=2t-1arrow_forward
- Use an algebraic method to eliminate the parameter and identify the graph of the parametric curve. x=8+t, y=t Previous The rectangular equation is y = x + A A = Type your answer...arrow_forwardFind the parametric equations for the line described below. the line through the point P(-7,0,7) and parallel to the line x=4t+7, y=2t-6, z=3t-6arrow_forwardFind parametric equations for the line described below.The line through the point P(-6, 0, -6) and parallel to the line x = 4t - 6, y=4t-1, z=2t-1arrow_forward
- Use parametric equations to model the path of a rider on the wheel. You want to end up with parametric equations, using t, that will give you the position of the rider every minute of the ride. Graph your results on a graphing calculator.A Ferris wheel has a diameter of 185 feet and sits 11 feet above the ground. It rotates in a counterclockwise direction, making one complete revolution every 15 minutes. Place your coordinate system so that the origin of the coordinate system is on the ground below the bottom of the wheel. x= _____________ y= _____________arrow_forwardFind the rectangular equation of the curve given by the parametric equations below. Then graph the curve and show its orientation. Assume that t can be any real number. x=t², y=-2t Rectangular equation: -8 -6 -4 -2 8- گیا 6- 4- 2- -2 -4 -6 -8 y V 2 4 6 8 x ve X X Ś 0=0 ? Ś ?arrow_forwardGraph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of the curve. x=6t2, y=t+4 negative infinity < t < infinityarrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning