/*! 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 33 Use a graphing utility to graph ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 33

Use a graphing utility to graph the polar equation. Identify the graph. \(r=\frac{14}{14+17 \sin \theta}\)

Short Answer

Expert verified
The graph shows a lima莽on, a type of polar graph usually having a loop. But in this particular equation, the analysis doesn't suggest any loop because the values in fraction don't fulfill the condition of lima莽on with inner loop.

Step by step solution

01

Understand the Polar Equation

To start with, look at the polar equation that says \( r = \frac{14}{14 + 17 \sin \theta}\). This expresses the radius, r (distance from the origin), in terms of an angle, \(\theta\).
02

Use a Graphing Utility

Next, input the polar equation into a graphing utility, which you can find online or through a calculator with graphic capabilities. Be sure to have the calculator in polar mode. Input the equation and have it create a range for \(\theta\), typically from 0 to \(2\pi\), that will cover all possible radians values.
03

Analyze Graph

Take a look at the graph generated. Polar plots often have unique shapes, compared to standard x-y plots. Try to identify what the plot represents.

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

Find the standard form of the equation of the ellipse with the given characteristics. Vertices: (0,2),(8,2)\(;\) minor axis of length 2

Find the standard form of the equation of the ellipse with the given characteristics. Center: (0,4)\(; a=2 c ;\) vertices: (-4,4),(4,4)

Find the vertex, focus, and directrix of the parabola. Use a graphing utility to graph the parabola. \(x^{2}+4 x+6 y-2=0\)

Find the vertex, focus, and directrix of the parabola. Use a graphing utility to graph the parabola. \(x^{2}-2 x+8 y+9=0\)

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. \(3 x^{2}+y^{2}+18 x-2 y-8=0\)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Mechanics Maths

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.