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...
Related questions
Question
100%
Convert the Parametric equation from Cartesian
![The image shows a mathematical expression in the form of parametric equations and a domain for the parameter \( t \):
b)
\[
\begin{cases}
x = -1 + \sec t \\
y = 2 + \tan t
\end{cases}
\]
The parameter \( t \) is defined over the interval:
\[
-\frac{\pi}{2} < t < \frac{\pi}{2}
\]
These equations are parametric, where:
- \( x \) is expressed in terms of \( t \) as \(-1 + \sec t\).
- \( y \) is expressed in terms of \( t \) as \(2 + \tan t\).
The parameter \( t \) lies in the open interval from \(-\frac{\pi}{2}\) to \(\frac{\pi}{2}\), which excludes the points where tangent and secant are undefined (specifically, where \( \cos t = 0 \)). This is because secant and tangent can have vertical asymptotes in those regions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb497b8c4-4d07-4c4c-ac55-469da516b240%2Fa50c070f-e534-4a65-baad-21f02147427c%2Fbu0npph_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image shows a mathematical expression in the form of parametric equations and a domain for the parameter \( t \):
b)
\[
\begin{cases}
x = -1 + \sec t \\
y = 2 + \tan t
\end{cases}
\]
The parameter \( t \) is defined over the interval:
\[
-\frac{\pi}{2} < t < \frac{\pi}{2}
\]
These equations are parametric, where:
- \( x \) is expressed in terms of \( t \) as \(-1 + \sec t\).
- \( y \) is expressed in terms of \( t \) as \(2 + \tan t\).
The parameter \( t \) lies in the open interval from \(-\frac{\pi}{2}\) to \(\frac{\pi}{2}\), which excludes the points where tangent and secant are undefined (specifically, where \( \cos t = 0 \)). This is because secant and tangent can have vertical asymptotes in those regions.
Expert Solution
Step 1
To convert the given parametric equation to Cartesian form.
Step by step
Solved in 2 steps with 1 images
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