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Q25.

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Precalculus Mathematics for Calculus

Found in: Page 593

Book edition 7th Edition

Author(s) James Stewart, Lothar Redlin, Saleem Watson

Pages 948 pages

ISBN 9781337067508

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Short Answer

Rectangular Coordinates to Polar Coordinates. A point is graphed in rectangular form. Find polar coordinates for the point, with $r > 0$ and $0 < θ < 2 π$

The polar coordinates are $3 \sqrt{2}, \frac{3 π}{4}$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

A point in the rectangular coordinate system

Step 2. Concept used

Four points match the polar coordinates of a point. The radius of each point is four units. Their angles are the only thing that separates them. As a result, find the point that has the same angle as the specified point..

Step 3. Calculation

The coordinates of the point are. So, $x = - 3$ and $y = 3$ . Now convert it into polar coordinates.

Use the formulae as-

$\begin{array}{l} r^{2} = x^{2} + y^{2} \\ \tan θ = \frac{y}{x} \end{array}$

$\begin{array}{l} \Rightarrow r^{2} = x^{2} + y^{2} \\ \Rightarrow r^{2} Invalid <m:msup> element Invalid <m:msup> element = + \\ \Rightarrow r^{2} = 18 \\ \Rightarrow r = \pm \sqrt{18} o r \pm 3 \sqrt{2} \end{array}$

But they had given, $r > 0$

Therefore, $r = + 3 \sqrt{2}$

The value of angle can be determined as-

$\begin{array}{l} \Rightarrow \tan θ = \frac{y}{x} \\ \Rightarrow \tan θ = \frac{3}{- 3} \\ \Rightarrow \tan θ = - 1 \\ \Rightarrow θ = \tan^{- 1} (- 1) \\ \Rightarrow θ = \frac{3 π}{4}, \frac{7 π}{4} \end{array}$

But in the question, $0 < θ < 2 π$ . Therefore $θ = \frac{3 π}{4}$

Polar coordinates of the point are $3 \sqrt{2}, \frac{3 π}{4}$

Most popular questions for Math Textbooks

Rectangular Coordinates to Polar Coordinates A point is graphed in rectangular form. Find polar coordinates for the point, with $r > 0$ and $0 < θ < 2 π$ .

Polar Equations to Rectangular Equations

Convert the polar equation to rectangular coordinates

$r^{2} = \sin 2 θ$

Write the vector v in the form ai + bj , given its magnitude ||v|| and the angle a it makes with the positive x-axis.

||v|| = 5, $α$ = 60 $°$

Points in Polar Coordinates Determine which point in the figure, $P, Q, R & S$ , has the given polar coordinates $- 4, \frac{101 π}{4}$

Polar Equations to Rectangular Equations

Convert the polar equation to rectangular coordinates

$r = 7$

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