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Find the unit tangent vector to the curve defined by 3πT 4 F(t) = (4 cos(t), 4 sin(t), 5 sin²(t)) at t = 3T 4

Find the unit tangent vector to the curve defined by 3πT 4 F(t) = (4 cos(t), 4 sin(t), 5 sin²(t)) at t = 3T 4

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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## Find the Unit Tangent Vector **Objective:** Determine the unit tangent vector to the curve defined by \( \vec{r}(t) = \langle 4 \cos(t), 4 \sin(t), 5 \sin^2(t) \rangle \) at \( t = \frac{3\pi}{4} \). ### Problem Statement To find the unit tangent vector \( \vec{T} \left( \frac{3\pi}{4} \right) \) at the specified parameter value. **Helpful Resource:** A video is available for additional guidance on solving this type of problem. [Submit your response](#) **Note:** Graphs or diagrams are not present in this problem.
Transcribed Image Text:## Find the Unit Tangent Vector **Objective:** Determine the unit tangent vector to the curve defined by \( \vec{r}(t) = \langle 4 \cos(t), 4 \sin(t), 5 \sin^2(t) \rangle \) at \( t = \frac{3\pi}{4} \). ### Problem Statement To find the unit tangent vector \( \vec{T} \left( \frac{3\pi}{4} \right) \) at the specified parameter value. **Helpful Resource:** A video is available for additional guidance on solving this type of problem. [Submit your response](#) **Note:** Graphs or diagrams are not present in this problem.
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