Find the unit tangent vector to the curve defined by r(t) = (4 cos(t), 4 sin(t), 2 sin²(t)) π at t = 2* T (7) = Use the unit tangent vector to write the parametric equations of a tangent line to the curve at t = 2 x(t) = y(t) z(t) TE = KIN π
Find the unit tangent vector to the curve defined by r(t) = (4 cos(t), 4 sin(t), 2 sin²(t)) π at t = 2* T (7) = Use the unit tangent vector to write the parametric equations of a tangent line to the curve at t = 2 x(t) = y(t) z(t) TE = KIN π
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Vector Calculus Problem
#### Problem Statement
Find the unit tangent vector to the curve defined by
\[ \vec{r}(t) = \langle 4 \cos(t), 4 \sin(t), 2 \sin^2(t) \rangle \]
at \( t = \frac{\pi}{2} \).
\[
\vec{T}\left( \frac{\pi}{2} \right) = \underline{\hspace{3cm}}
\]
Use the unit tangent vector to write the parametric equations of a tangent line to the curve at \( t = \frac{\pi}{2} \).
\[
\begin{aligned}
x(t) &= \underline{\hspace{3cm}} \\
y(t) &= \underline{\hspace{3cm}} \\
z(t) &= \underline{\hspace{3cm}} \\
\end{aligned}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F74b6836e-7075-4604-8b7e-b1441272473c%2F4ea1ab0d-e42b-4fea-9194-e57b02551695%2F7poi8ri_processed.png&w=3840&q=75)
Transcribed Image Text:### Vector Calculus Problem
#### Problem Statement
Find the unit tangent vector to the curve defined by
\[ \vec{r}(t) = \langle 4 \cos(t), 4 \sin(t), 2 \sin^2(t) \rangle \]
at \( t = \frac{\pi}{2} \).
\[
\vec{T}\left( \frac{\pi}{2} \right) = \underline{\hspace{3cm}}
\]
Use the unit tangent vector to write the parametric equations of a tangent line to the curve at \( t = \frac{\pi}{2} \).
\[
\begin{aligned}
x(t) &= \underline{\hspace{3cm}} \\
y(t) &= \underline{\hspace{3cm}} \\
z(t) &= \underline{\hspace{3cm}} \\
\end{aligned}
\]
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