/*! 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 32 Use a graphing utility to graph ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 32

Use a graphing utility to graph the polar equation. Identify the graph. \(r=\frac{4}{1-2 \cos \theta}\)

Short Answer

Expert verified
Using a graphing utility, we can graph given polar equation. Once graphed, by comparing the output to common polar graph shapes, we can identify what kind of graph we have. For this exercise, the result is a type of lima莽on, due to the general form of the equation and the graphical representation.

Step by step solution

01

Understand the Polar Equation

Given the polar equation, \(r=\frac{4}{1-2 \cos \theta}\), we see that it represents a mathematical relation between the distance of the point from the origin (r) and the angle \(\theta\) the line connecting the point and origin makes with positive x-axis.
02

Plot the Graph

To plot this equation, we will use a graphing utility like a graphing calculator or software like Desmos. On the x-axis, we denote \(\theta\) and on the y-axis, we denote \(r\). We input the equation, \(r=\frac{4}{1-2 \cos \theta}\) in the graphing utility and plot the polar graph.
03

Identify the Graph

After plotting the equation, we look at the shape that the graph gives. We can compare this with the common types of polar graphs like circles, spirals, rose curves, and lemniscates in order to correctly identify our graph.

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

Identify the conic as a circle or an ellipse. Then find the center, radius, vertices, foci, and eccentricity of the conic (if applicable), and sketch its graph. . \(x^{2}+y^{2}-4 x+6 y-3=0\)

Identify the conic as a circle or an ellipse. Then find the center, radius, vertices, foci, and eccentricity of the conic (if applicable), and sketch its graph. \(\frac{(x+3)^{2}}{12}+\frac{(y-2)^{2}}{16}=1\)

Determine whether the statement is true or false. Justify your answer. If the vertex and focus of a parabola are on a horizontal line, then the directrix of the parabola is vertical.

Each cable of the Golden Gate Bridge is suspended (in the shape of a parabola) between two towers that are 1280 meters apart. The top of each tower is 152 meters above the roadway. The cables touch the roadway midway between the towers. (a) Draw a sketch of the bridge. Locate the origin of a rectangular coordinate system at the center of the roadway. Label the coordinates of the known points. (b) Write an equation that models the cables. (c) Complete the table by finding the height \(y\) of the suspension cables over the roadway at a distance of \(x\) meters from the center of the bridge. $$\begin{array}{|c|c|}\hline \text { Distance, } \boldsymbol{x} & \text { Height, } \boldsymbol{y} \\\\\hline 0 & \\\100 & \\\250 & \\\400 & \\\500 & \\\\\hline\end{array}$$

Identify the conic as a circle or an ellipse. Then find the center, radius, vertices, foci, and eccentricity of the conic (if applicable), and sketch its graph. \(6 x^{2}+2 y^{2}+18 x-10 y+2=0\)
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

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.