Answered: Convert (-3, 3) to polar coordinates…

Math

Trigonometry

Convert (-3, 3) to polar coordinates with r positive and u between 0 and 2p.

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.7: Polar Coordinates

Problem 4ECP

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Question

Convert (-3, 3) to polar coordinates with r positive and u between 0 and 2p.

Expert Solution

Step 1

Given point in cartesian co-ordinate system:

(-3, 3)

Step 2

To convert from Cartesian Coordinates (x, y) to Polar Coordinates (r,θ):

$r = \sqrt{x^{2} + y^{2}}$

and $θ$ is given quadrant wise as below:

Quadrant	(x, y)	$θ$ in radian
I	x>0, y>0	$\tan^{- 1} (\frac{y}{x})$
II	x<0, y>0	$π + \tan^{- 1} (\frac{y}{x})$
III	x<0, y<0	$π + \tan^{- 1} (\frac{y}{x})$
IV	x>0, y< 0	$2 π + \tan^{- 1} (\frac{y}{x})$

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