(x = -1 + sect b) { y = 2 + tant -<< 2 2

Calculus: Early Transcendentals
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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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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.
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.
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