Question

Consider the parametric curve defined by x = 5cos^2(t) and y = sin(t). a.) Find all the values of t where the parametric curve has a horizontal or vertical tangent line. b.) Find all the values of t where the tangent line has a slope of 1. c.) Find a Cartesian equation for the parametric curve and sketch its graph.

Name: consider the parametric defined by x5cos2t and ysint a find all the values of t where the parametric curve has a horizontal or vertical tangent line b find all the values of t where the tang 26044
Uploaded: 2022-06-28T16:10:18-08:00
Duration: 4 min 19 s
Channel: Madhur L
Description: consider the parametric defined by x5cos2t and ysint a find all the values of t where the parametric curve has a horizontal or vertical tangent line b find all the values of t where the tang 26044

          Consider the parametric curve defined by x = 5cos^2(t) and y = sin(t).
a.) Find all the values of t where the parametric curve has a horizontal or vertical tangent line.
b.) Find all the values of t where the tangent line has a slope of 1.
c.) Find a Cartesian equation for the parametric curve and sketch its graph.

Added by Asunci-N L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

06/28/2022

Step 1

\[ \frac{dy}{dx} = -\frac{1}{10} \sin(t) = 0 \] This implies \( \sin(t) = 0 \), which occurs at \( t = n\pi \) where \( n \) is an integer. ** Show more…

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Consider the parametric curve defined by x = 5cos^2(t) and y = sin(t). a.) Find all the values of t where the parametric curve has a horizontal or vertical tangent line. b.) Find all the values of t where the tangent line has a slope of 1. c.) Find a Cartesian equation for the parametric curve and sketch its graph.