The rectangular coordinates of a point are (4, −4). Plot the point and find two sets of polar coordinates for the point for 0 < 2.

Question

The rectangular coordinates of a point are (4, −4). Plot the point and find two sets of polar coordinates for the point for 0 < 2.

waigaK 2021-02-04 Answered

The rectangular coordinates of a point are (4, −4). Plot the point and find two sets of polar coordinates for the point for

0 < 2

.

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Expert Answer

dieseisB

Answered 2021-02-05 Author has 85 answers

Given, $(x, y) = (4, - 4)$ For the polar coordinates $r = \sqrt{x^{2} + y^{2}} a n d θ = t a n^{-} 1 (\frac{y}{x})$
$r = \sqrt{16 + 16}$
$r = \sqrt{32}$
$r = 4 \sqrt{2}$ And $θ = t a n^{-} 1 (\frac{- 4}{4}$
$θ = t a n^{-} 1 (- 1)$
$θ = \frac{π}{4}$ The two sets of polar coordinates are $(- 4 \sqrt{2}, \frac{π}{4}) . (4 \sqrt{2}, \frac{π}{4})$

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