Find dy/dx and d²y/dx2, and find the slope and concavity (if possible) at the given value of the parameter. (If an answer does not exist, enter DNE. Parametric Equations Point x = 6 cos 0, y = 6 sin 0 %3D dx d2y %3D dx2 slope concavity: --Select--

Find dy/dx and d²y/dx2, and find the slope and concavity (if possible) at the given value of the parameter. (If an answer does not exist, enter DNE. Parametric Equations Point x = 6 cos 0, y = 6 sin 0 %3D dx d2y %3D dx2 slope concavity: --Select--

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section: Chapter Questions

Problem 45CT

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Question

Find dy/dx and d'y/dx2, and find the slope and concavity (if possible) at the given value of the parameter. (If an answer does not exist, enter DNE.)
Parametric Equations
Point
x = 6 cos 0, y = 6 sin 0
4
dy
%3D
dx
d2y
%3D
dx2
slope
concavity:
Select-

Expert Solution

Step 1

We are given the parametric equations:

$x = 6 \cos (θ) y = 6 \sin (θ)$

We know that the derivative of $\cos (a) = - \sin (a)$ and the derivative of $\sin (a) = \cos (a)$ .

$d x = d (6 \cos (θ)) d x = - 6 \sin (θ) d y = d (6 \sin (θ)) d y = 6 \cos (θ)$

$d x = - 6 \sin (θ) d y = 6 \cos (θ)$

$d^{2} x = - 6 \cos (θ) d^{2} y = - 6 \sin (θ)$

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