Q. 86 Explain how you proceed to conve... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 9: Q. 86 (page 568)

Explain how you proceed to convert from rectangular coordinates to polar coordinates.

Short Answer

Expert verified

To convert from rectangular coordinates to polar coordinates use the formula $r = \sqrt{x^{2} + y^{2}} a n d 胃 = \tan^{- 1} \frac{y}{x} .$

Step by step solution

Step 1. Given Information

The points $(r, 胃)$ are determined by their angle on the unit circle and their distance from the origin in the polar coordinates.

The points $(x, y)$ are determined by their distance from the xand yaxes in the rectangular coordinates.

Step 2. Explaining

As we know if a point Pwith polar coordinates are $(r, 胃)$ , the rectangular coordinates $(x, y)$ of Pare given by $x = r \cos 胃 y = r \sin 胃$

Now, square and add both equations

$x^{2} + y^{2} = {(r \cos 胃)}^{2} + {(r \sin 胃)}^{2} x^{2} + y^{2} = r^{2} (\cos^{2} 胃 + \sin^{2} 胃) x^{2} + y^{2} = r^{2} [\cos^{2} 胃 + \sin^{2} 胃 = 1] r = \sqrt{x^{2} + y^{2}}$

And as we know

$\tan 胃 = \frac{y}{x} S o, 胃 = \tan^{- 1} \frac{y}{x}$

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91影视

Explain how you proceed to convert from rectangular coordinates to polar coordinates.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explaining

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