/*! 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 27 Use a graphing utility to find t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 27

Use a graphing utility to find the rectangular coordinates of the point given in polar coordinates. Round your results to two decimal places. $$(2,2 \pi / 9)$$

Short Answer

Expert verified
The rectangular coordinates of the polar point given as \((2, 2 \pi / 9)\) are approximately \((1.72, 0.76)\), given that the results are rounded to two decimal places.

Step by step solution

01

Set Up the Equations

Identify the given polar coordinates \(r\), the radial coordinate, and \(\theta\), the angular coordinate. In this case, \(r = 2\) and \(\theta = 2 \pi / 9\). Now, set up the equations using \(x = r \cos(\theta)\) and \(y = r \sin(\theta)\) to convert these polar coordinates into rectangular coordinates.
02

Calculate x-coordinate

To find the x-coordinate, substitute the given values into the equation \(x = r \cos(\theta)\). So, we get \(x = 2 \cos(2 \pi / 9)\). Now, use a calculator to find the numerical value of \(x\) and round your result to two decimal places.
03

Calculate y-coordinate

To calculate the y-coordinate, substitute the given values into the equation \(y = r \sin(\theta)\). Therefore, \(y = 2 \sin(2 \pi / 9)\). To get a numerical value for \(y\), again use a calculator and round your result to two decimal places.

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 a polar equation of the conic with its focus at the pole. $$\begin{array}{cc} \text{Conic} & \text{Vertex or Vertices} \\\ \text{Ellipse} &\left(2, \frac{\pi}{2}\right),\left(4, \frac{3 \pi}{2}\right)\end{array}$$

Find the zeros (if any) of the rational function. $$f(x)=5-\frac{3}{x-2}$$

Identify the type of conic represented by the equation. Use a graphing utility to confirm your result. $$r=\frac{10}{3+9 \sin \theta}$$

Convert the rectangular equation to polar form. Assume \(a<0\) $$3 x-y+2=0$$

Determine whether the statement is true or false. Justify your answer. If \(\left(r, \theta_{1}\right)\) and \(\left(r, \theta_{2}\right)\) represent the same point in the polar coordinate system, then \(\theta_{1}=\theta_{2}+2 \pi n\) for some integer \(n\).
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

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.