/*! 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 36 Polar coordinates of a point are... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 36

Polar coordinates of a point are given. Find the rectangular coordinates of each point. $$\left(2, \frac{\pi}{6}\right)$$

Short Answer

Expert verified
The rectangular coordinates of the point are \((\sqrt{3}, 1)\)

Step by step solution

01

Identify the polar coordinates

The polar coordinates given are \((2, \frac{\pi}{6})\), where \(r = 2\) and \(\theta= \frac{\pi}{6}\).
02

Apply the conversion formulae

For the x-coordinate, compute \(x = 2\cos(\frac{\pi}{6})\).The cosine of \(\frac{\pi}{6}\) is \(\frac{\sqrt{3}}{2}\), so the x-coordinate is \(x = 2 \times \frac{\sqrt{3}}{2} = \sqrt{3}\).For the y-coordinate, calculate \(y = 2\sin(\frac{\pi}{6})\).The sine of \(\frac{\pi}{6}\) is \(\frac{1}{2}\), so the y-coordinate is \(y = 2 \times \frac{1}{2} = 1\).
03

Report the rectangular coordinates

The rectangular coordinates of the point are \((\sqrt{3}, 1)\).

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

Graph: \(\quad f(x)=\frac{4 x-4}{x-2}\)

A force of 4 pounds acts in the direction of \(50^{\circ}\) to the horizontal. The force moves an object along a straight line from the point (3,7) to the point \((8,10),\) with distance measured in feet. Find the work done by the force.

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.

Find \(\text {pro}_{\mathbf{w}} \mathbf{V}\) Then decompose v into two vectors, \(\mathbf{v}_{1}\) and \(\mathbf{v}_{2},\) where \(\mathbf{v}_{1}\) is parallel to \(\mathbf{w}\) and \(\mathbf{v}_{2}\) is orthogonal to \(\mathbf{w}.\) $$\mathbf{v}=3 \mathbf{i}-2 \mathbf{j}, \quad \mathbf{w}=2 \mathbf{i}+\mathbf{j}$$

Find \(\text {pro}_{\mathbf{w}} \mathbf{V}\) Then decompose v into two vectors, \(\mathbf{v}_{1}\) and \(\mathbf{v}_{2},\) where \(\mathbf{v}_{1}\) is parallel to \(\mathbf{w}\) and \(\mathbf{v}_{2}\) is orthogonal to \(\mathbf{w}.\) $$\mathbf{v}=\mathbf{i}+3 \mathbf{j}, \quad \mathbf{w}=-2 \mathbf{i}+5 \mathbf{j}$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Probability and Statistics

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.