-1.5Need Help?I-1.0 -0.5whereRead It0.5-0.5-1.0-1.5Watch It0.5(b) Find a rectangular-coordinate equation for the curve by eliminating the parameter.1.0≤ x ≤1.5X-1.5 -1.0 -0. A pair of parametric equations is given.x = sin²(t), y = sin(t)(a) Sketch the curve represented by the parametric equations. Use arrows to indicate the direction of the curve as t increases.yy-1.5 -1.0 -0.5-1.5-1.01.51.00.5-0.5-0.5-1.0-1.5y1.51.00.50.5 1.0 1.50.51.0- X1.5X-1.5 -1.0 -0.5-1.5 -1.0-0.51.51.00.5-0.5-1.0-1.51.5y1.00.50.50.5 1.0 1.50.51.01.5XX

Answered: -1.5 Need Help? I -1.0 -0.5 where Read…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter8: Polar Coordinates And Parametric Equations

Section8.4: Plane Curves And Parametric Equations

Problem 40E

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Similar questions

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.
Epicycloid If the circle C of Exercise 63 rolls on the outside of the larger circle, the curve traced out by P is called an epicycloid. Find parametric equations for the epicycloid. Hypocycloid A circle C of radius b rolls on the inside of a larger circle of radius a centered at the origin. Let P be a fixed point on the smaller circle, with the initial position at the point (a,0) as shown in the figure. The curve traced out by P is called a hypocycloid. a Show that parametric equations of hypocycloid are x=(ab)cos+bcos(abb) y=(ab)sinbsin(abb) b If a=4b, the hypocycloid is called an asteroid. Show that in this case parametric equations can be reduced to x=acos3y=asin3 Sketch the curve. Eliminate the parameter to obtain an equation for the asteroid in rectangular coordinates.
Shooting into the Wind Using the parametric equations you derived in Problem 6. draw graphs of the path of a projectile with initial speed v0=32ft/s, fired into a headwind of =24ft/s, for the angles =5,15,30,40,45,55,60 and 75. Is it still true that the greatest range is attained when firing at 45 ? Draw some more graphs for different angles, and use these graphs to estimate the optimal firing angle.

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-1.5 Need Help? I -1.0 -0.5 where Read It 0.5 -0.5 -1.0 -1.5 Watch It 0.5 (b) Find a rectangular-coordinate equation for the curve by eliminating the parameter. 1.0 ≤ x ≤ 1.5 X -1.5 -1.0 -0.