See image for question A motion is defined by the following parametric equations.x = -sin(t), y = 2cos(t),-π≤t≤ πd²ydx²(a) Show that the particle passes through the point(b) Find the slope of the tangent line to the curve (the orbit) at this point.(c) By using(√2/2₁ √₂) . Find the time t at which the particle passes through this point.determine whether the orbit is concave up or concave down near this point.(d) At what speed does the particle go through this point?(e) Sketch the orbit and indicate the direction of the motion.

These are multiple sub parts and we can do maximum 3 sub parts so i am doing first 3 sub parts here.…

A motion is defined by the following parametric equations. x = -sin(t), y = 2cos(t), -πst≤ π (a) Show that the particle passes through the point (1/1/2₁ √2) . Find the time t at which the particle passes through this point. (b) Find the slope of the tangent line to the curve (the orbit) at this point. d²y dx² (c) By using determine whether the orbit is concave up or concave down near this point.

A motion is defined by the following parametric equations. x = -sin(t), y = 2cos(t), -πst≤ π (a) Show that the particle passes through the point (1/1/2₁ √2) . Find the time t at which the particle passes through this point. (b) Find the slope of the tangent line to the curve (the orbit) at this point. d²y dx² (c) By using determine whether the orbit is concave up or concave down near this point.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 35E

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