Find the parametric eque tangent line at the poi (Cos (5/6 T)), Sin (5/ π), Z=Cost₁ y = Sint₁ Z= €²(+) = 1 754 4629L1= Z(+1=
Find the parametric eque tangent line at the poi (Cos (5/6 T)), Sin (5/ π), Z=Cost₁ y = Sint₁ Z= €²(+) = 1 754 4629L1= Z(+1=
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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Can anyone please help me to solve this problem please? I am stuck!
![**Title: Finding Parametric Equations for a Tangent Line**
**Objective:**
To find the parametric equations for the tangent line at a given point on the curve.
**Given Curve:**
- Parametric equations:
- \( z = t \)
- \( y = \sin t \)
**Point of Tangency:**
- \( \left( \cos\left(\frac{5\pi}{6}\right), \sin\left(\frac{5\pi}{6}\right), \frac{5\pi}{6} \right) \)
**Task:**
Find the parametric equations for the tangent line at this point.
**Setup for Tangent Line:**
1. The tangent line will be represented as:
- \( x(t) = \) [expression]
- \( y(t) = \) [expression]
- \( z(t) = \) [expression]
**Graph/Diagram Explanation:**
There are no graphs or diagrams present in the text. The objective is to find the parametric representation of the tangent line at the specified point on the curve, defined by trigonometric functions.
**Conclusion:**
To solve the problem, we need to determine the derivatives involved and substitute the given point into the tangent line equations to find the expressions \( x(t), y(t), \) and \( z(t) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F99d15f92-0bff-4b4d-a47e-2ac33d144271%2F150530c6-589f-48b5-95b2-789118e97bce%2F2zyz8em_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Finding Parametric Equations for a Tangent Line**
**Objective:**
To find the parametric equations for the tangent line at a given point on the curve.
**Given Curve:**
- Parametric equations:
- \( z = t \)
- \( y = \sin t \)
**Point of Tangency:**
- \( \left( \cos\left(\frac{5\pi}{6}\right), \sin\left(\frac{5\pi}{6}\right), \frac{5\pi}{6} \right) \)
**Task:**
Find the parametric equations for the tangent line at this point.
**Setup for Tangent Line:**
1. The tangent line will be represented as:
- \( x(t) = \) [expression]
- \( y(t) = \) [expression]
- \( z(t) = \) [expression]
**Graph/Diagram Explanation:**
There are no graphs or diagrams present in the text. The objective is to find the parametric representation of the tangent line at the specified point on the curve, defined by trigonometric functions.
**Conclusion:**
To solve the problem, we need to determine the derivatives involved and substitute the given point into the tangent line equations to find the expressions \( x(t), y(t), \) and \( z(t) \).
![**Task: Find the parametric equations for the tangent line at the point \((\cos(\frac{5\pi}{6}), \sin(\frac{5\pi}{6}), \frac{5\pi}{6})\) on the curve.**
Given:
- \(x = \cos t\)
- \(y = \sin t\)
- \(z = t\)
Calculate:
- \(\frac{dz}{dt} =\) [Blank Box]
- \(\frac{dx}{dt} =\) [Blank Box]
- \(\frac{dy}{dt} =\) [Blank Box]
- \(\frac{dz}{dy} =\) [Blank Box]
- \(\frac{dz}{dx} =\) [Blank Box]
This exercise involves differentiating parametric equations to find the slope of the tangent line at a specific point on the curve.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F99d15f92-0bff-4b4d-a47e-2ac33d144271%2F150530c6-589f-48b5-95b2-789118e97bce%2F0yp2ghq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Task: Find the parametric equations for the tangent line at the point \((\cos(\frac{5\pi}{6}), \sin(\frac{5\pi}{6}), \frac{5\pi}{6})\) on the curve.**
Given:
- \(x = \cos t\)
- \(y = \sin t\)
- \(z = t\)
Calculate:
- \(\frac{dz}{dt} =\) [Blank Box]
- \(\frac{dx}{dt} =\) [Blank Box]
- \(\frac{dy}{dt} =\) [Blank Box]
- \(\frac{dz}{dy} =\) [Blank Box]
- \(\frac{dz}{dx} =\) [Blank Box]
This exercise involves differentiating parametric equations to find the slope of the tangent line at a specific point on the curve.
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