/*! 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 26 A point in rectangular coordinat... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 26

A point in rectangular coordinates is given. Convert the point to polar coordinates. $$(5,12)$$

Short Answer

Expert verified
The polar coordinates equivalent of the rectangular coordinates (5,12) is approximately (13, \(arctan(\frac{12}{5})\)). The exact values will depend on the calculator used to compute arctan.

Step by step solution

01

Calculate the radius

We can find the radius using the formula \(r = \sqrt{x^2 + y^2}\). In this case, our x is 5 and our y is 12. Therefore, \(r = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13.\)
02

Calculate the angle

The angle or theta is found using the formula \(theta = arctan(\frac{y}{x})\), where x and y are the values from the rectangular coordinate. For this particular point (5,12), the theta becomes \(arctan(\frac{12}{5})\). Calculate the arctan of this fraction to get the angle in radians. Alternatively, we can use a calculator to obtain the angle in degrees.
03

Put the polar coordinate together

Now we combine the calculated radius and angle together to get the polar coordinate. It should be presented in the format (r, theta).

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

In Exercises 79-82, find the exact value of the trigonometric function given that \(u\) and \(v\) are in Quadrant IV and \(\sin u=-\frac{3}{5}\) and \(\cos v=1 / \sqrt{2}\). $$ \cos (u-v) $$

\(r=2 \sec \theta\)

True or False? In Exercises 57 and 58, determine whether the statement is true or false. Justify your answer. In the polar coordinate system, if a graph that has symmetry with respect to the polar axis were folded on the line \(\theta=0\), the portion of the graph above the polar axis would coincide with the portion of the graph below the polar axis.

\(r^{2}=9 \cos 2 \theta\)

In Exercises 29-32, use a graphing utility to graph the rotated conic. $$ r=\frac{3}{3+\sin (\theta-\pi / 3)} $$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

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.