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Precalculus Mathematics for Calculus
Found in: Page 593
Precalculus Mathematics for Calculus

Precalculus Mathematics for Calculus

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>0and 0<θ<2π

The polar coordinates are32,3π4

See the step by step solution

Step by Step Solution

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-


r2=x2+y2r2Invalid <m:msup> elementInvalid <m:msup> element=+r2=18r=±18or±32

But they had given,r>0

Therefore, r=+32

The value of angle can be determined as-


But in the question,0<θ<2π . Therefore θ=3π4

Polar coordinates of the point are 32,3π4

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