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Q29.

Expert-verified

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

Polar Coordinates to Rectangular Coordinates Find the rectangular coordinates for the point whose polar coordinates are given. $(4, π / 6)$

The rectangular coordinates of the point $(4, \frac{π}{6})$ are. ${(2 \sqrt{3}, 2)}^{.}$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1.Given information.

The polar coordinates of the point are $(4, \frac{π}{6})$ .

Step 2. We can find the rectangular coordinates of the point using the polar to rectangular coordinates conversion formulas.

Since the polar coordinates are $(4, \frac{π}{6})$ , we can say that $r = 4$ and

$\begin{array}{l} θ = \frac{π}{6} \\ \Rightarrow x = r \cos θ \\ \Rightarrow x = 4 \cos (\frac{π}{6}) \\ \Rightarrow x = 4 \cdot (\frac{\sqrt{3}}{2}) \\ \Rightarrow x = 2 \sqrt{3} \end{array}$

Now, to find the value of y,

$\begin{array}{l} \Rightarrow y = r \sin θ \\ \Rightarrow y = 4 \sin (\frac{π}{6}) \\ \Rightarrow y = 4 \cdot (\frac{1}{2}) \\ \Rightarrow y = 2 \end{array}$

Most popular questions for Math Textbooks

Testing for Symmetry Test the polar equation for symmetry with respect to the polar axis, the pole, and the line $θ = π / 2$

. $r = 2 - \sin θ$

Rectangular Equations to Polar Equations

Convert the equation to polar form. $x^{2} + y^{2} = 9$

Testing for Symmetry Test the polar equation for symmetry concerning the polar axis, the pole, and the line $θ = π / 2$

$r = 4 + 8 \cos θ$ .

Rectangular Coordinates to Polar Coordinates Convert the rectangular coordinates to polar coordinates with $r > 0$ and $0 \leq θ < 2 π .$ $(- \sqrt{6}, - \sqrt{2})$ .

Plotting Points in Polar Coordinates Plot the point that has the given polar coordinates $(6, - \frac{7 π}{6})$

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