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
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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 \( t = \frac{\pi}{2} \).

\[
\begin{aligned}
x(t) &= \underline{\hspace{3cm}} \\
y(t) &= \underline{\hspace{3cm}} \\
z(t) &= \underline{\hspace{3cm}} \\
\end{aligned}
\]
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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