/*! 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 18 Use the angle feature of a graph... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 18

Use the angle feature of a graphing utility to find one set of polar coordinates for the point given in rectangular coordinates. $$ (0,-5) $$

Short Answer

Expert verified
The point (0, -5) in rectangular coordinates corresponds to (-5, -蟺/2 rad) in polar coordinates.

Step by step solution

01

Determine the Radial Coordinate

For any point (x,y), the radial coordinate r can be found using the Pythagorean theorem: r = sqrt(x^2 + y^2). In this case, r = sqrt(0^2 + (-5)^2) = sqrt(25) = 5. Because the point is below the x-axis, the radial coordinate will be -5 (distance is 5 units from origin but directed along the negative y-axis).
02

Calculate the Angular Coordinate

胃 = atan2(y, x), where atan2 is the two-argument arctangent function. But since x = 0, directly plugging into the formula would give a division by zero error. But as a special case, if x=0 and y is negative, then the angle 胃 is -90 degrees. Convert this to radians by multiplying by 蟺/180, 胃 = (-90 * 蟺) / 180 = -蟺/2 rad.

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

Write the equation for the ellipse rotated \(\pi / 4\) radian clockwise from the ellipse \(r=\frac{5}{5+3 \cos \theta}\).

In Exercises \(7-16,\) find the eccentricity and the distance from the pole to the directrix of the conic. Then sketch and identify the graph. Use a graphing utility to confirm your results. \(r=\frac{6}{1+\cos \theta}\)

Give the integral formulas for the area of the surface of revolution formed when the graph of \(r=f(\theta)\) is revolved about (a) the \(x\) -axis and (b) the \(y\) -axis.

In Exercises \(7-16,\) find the eccentricity and the distance from the pole to the directrix of the conic. Then sketch and identify the graph. Use a graphing utility to confirm your results. \(r=\frac{3}{2+6 \sin \theta}\)

Use a graphing utility to graph the curve represented by the parametric equations (indicate the orientation of the curve). Eliminate the parameter and write the corresponding rectangular equation. $$ \begin{array}{l} x=4+2 \cos \theta \\ y=-1+\sin \theta \end{array} $$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Logic and Functions

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.