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.

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

Answers (1)

2021-02-05

Given, \((x, y) = (4, −4)\) For the polar coordinates \(r = \sqrt{x^2 + y^2}\ and\ \theta = tan^−1 (\frac{y}{x})\)
\(r = \sqrt{16 + 16}\)
\(r = \sqrt{32}\)
\(r = 4 \sqrt 2\) And \(\theta = tan^-1 (\frac{-4}{4}\)
\(\theta = tan^-1 (-1)\)
\(\theta = \frac{\pi}{4}\) The two sets of polar coordinates are \((-4 \sqrt2, \frac{\pi}{4}). (4 \sqrt2, \frac{\pi}{4})\)

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