/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 29 Convert the following equations ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 29

Convert the following equations to Cartesian coordinates. Describe the resulting curve. $$r=2$$

Short Answer

Expert verified
Answer: The Cartesian coordinate equation for the polar coordinate equation r = 2 is x^2 + y^2 = 4. This equation represents a circle with a center at the origin (0, 0) and a radius of 2.

Step by step solution

01

Use conversion formulas to convert the polar equation to Cartesian coordinates

Since the given equation is r = 2, we will replace r with 2 in the conversion formulas: x = 2 * cos(胃) y = 2 * sin(胃)
02

Eliminate the 胃 variable to obtain a Cartesian equation.

To describe the resulting curve, we need a single Cartesian equation without 胃. We can achieve this by using the Pythagorean identity: sin^2(胃) + cos^2(胃) = 1. We start by finding formulas for sin^2(胃) and cos^2(胃) from our previous step: sin^2(胃) = (y/2)^2 cos^2(胃) = (x/2)^2 Now we can plug these formulas into the Pythagorean identity: (y/2)^2 + (x/2)^2 = 1
03

Simplify the resulting equation and describe the curve

We start by simplifying the equation: y^2/4 + x^2/4 = 1 To simplify further, we can multiply both sides by 4: y^2 + x^2 = 4 This is the equation of a circle in Cartesian coordinates with a center at the origin (0, 0) and a radius of 2.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The butterfly curve of Example 8 may be enhanced by adding a term: $$r=e^{\sin \theta}-2 \cos 4 \theta+\sin ^{5}(\theta / 12), \quad \text { for } 0 \leq \theta \leq 24 \pi$$ a. Graph the curve. b. Explain why the new term produces the observed effect.

How does the eccentricity determine the type of conic section?

Explain why the slope of the line tangent to the polar graph of \(r=f(\theta)\) is not \(d r / d \theta\)

Show that an ellipse and a hyperbola that have the same two foci intersect at right angles.

Consider the following parametric equations. a. Make a brief table of values of \(t, x,\) and \(y\) b. Plot the points in the table and the full parametric curve, indicating the positive orientation (the direction of increasing \(t\) ). c. Eliminate the parameter to obtain an equation in \(x\) and \(y\) d. Describe the curve. $$x=t^{3}-1, y=5 t+1 ;-3 \leq t \leq 3$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.