/*! 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 94 Graph \(r_{1}\) and \(r_{2}\) in... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 94

Graph \(r_{1}\) and \(r_{2}\) in the same polar coordinate system. What is the relationship between the two graphs? $$r_{1}=2 \sin 3 \theta, r_{2}=2 \sin 3\left(\theta+\frac{\pi}{6}\right)$$

Short Answer

Expert verified
Both graphs have the same shape as they are both 2 times the sine of 3 times an angle. However, the graph for \(r_{2}\) is shifted to the right by \(\frac{\pi}{6}\) radians compared to the graph for \(r_{1}\). This shift is simply due to the addition of \(\frac{\pi}{6}\) to the \(\theta\) in the equation for \(r_{2}\).

Step by step solution

01

Plotting the first equation

To plot \(r_{1}=2 \sin 3 \theta\), start by setting \(\theta\) to various values from 0 to \(2\pi\), calculate the corresponding \(r_{1}\) values, and plot these (\(r_{1}, \theta\)) coordinates on the polar coordinate system.
02

Plotting the second equation

Next, plot \(r_{2}=2 \sin 3\left(\theta + \frac{\pi}{6}\right)\) the same way. Remember \(\frac{\pi}{6}\) is a phase shift, meaning the entire graph of \(r_{2}\) is shifted \(\frac{\pi}{6}\) to the right compared tot he graph of \(r_{1}\). Plot these (\(r_{2}, \theta\)) coordinates on the same polar coordinate system.
03

Identify the relationship

Identify the relationship between the two graphs based on their shape and position. The graph of \(r_{2}\) is a phase-shifted version of the graph of \(r_{1}\), meaning they have the same shape, but \(r_{2}\) is shifted to the right by \(\frac{\pi}{6}\).

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

Determine the amplitude, period, and phase shift of \(y=3 \cos (2 x+\pi) .\) Then graph one period of the function.

Find the work done when a crane lifts a 6000-pound boulder through a vertical distance of 12 feet. Round to the nearest foot-pound.

A force is given by the vector \(\mathbf{F}=5 \mathbf{i}+7 \mathbf{j} .\) The force moves an object along a straight line from the point (8,11) to the point \((18,20) .\) Find the work done if the distance is measured in meters and the force is measured in newtons.

What are orthogonal vectors?

Find two vectors \(\mathbf{v}\) and \(\mathbf{w}\) such that the projection of \(\mathbf{v}\) onto \(\mathbf{w}\) is \(\mathbf{v}\).
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Pure 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.