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Chapter 11: Problem 1

Express the polar equation \(r=f(\theta)\) in parametric form in Cartesian coordinates, where \(\theta\) is the parameter.

Short Answer

Expert verified
Question: Convert the given polar equation r = f(胃) into parametric form in Cartesian coordinates. Answer: The parametric form of the given polar equation in Cartesian coordinates is: x(胃) = f(胃)cos(胃) and y(胃) = f(胃)sin(胃).

Step by step solution

01

Write down the given polar equation

The given polar equation is r = f(胃).
02

Write down the Cartesian coordinate relationships

We will use the polar-to-Cartesian coordinate relationships: x = rcos(胃) y = rsin(胃)
03

Substitute the polar equation into the Cartesian coordinate relationships

Replace r in the Cartesian coordinate relationships with f(胃): x(胃) = f(胃)cos(胃) y(胃) = f(胃)sin(胃)
04

Write down the parametric form in Cartesian coordinates

The parametric form of the given polar equation in Cartesian coordinates is: x(胃) = f(胃)cos(胃) y(胃) = f(胃)sin(胃) So, the given polar equation r = f(胃) has been expressed in parametric form in Cartesian coordinates.

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Most popular questions from this chapter

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Let \(H\) be the right branch of the hyperbola \(x^{2}-y^{2}=1\) and let \(\ell\) be the line \(y=m(x-2)\) that passes through the point (2,0) with slope \(m,\) where \(-\inftyu(m)>1 .\) For what values of \(m\) are there two intersection points? b. Evaluate \(\lim _{m \rightarrow 1^{+}} u(m)\) and \(\lim _{m \rightarrow 1^{+}} v(m)\) c. Evaluate \(\lim _{m \rightarrow \infty} u(m)\) and \(\lim _{m \rightarrow \infty} v(m)\) d. Evaluate and interpret \(\lim _{m \rightarrow \infty} A(m)\)

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