The rectangular coordinates of a point are given (-5, 2) . Use a graphing utility in radian mode to find polar coordinates of each point to three decimal places.

The rectangular coordinates of a point are given (-5, 2) . Use a graphing utility in radian mode to find polar coordinates of each point to three decimal places.

Question
The rectangular coordinates of a point are given \((-5, 2)\) . Use a graphing utility in radian mode to find polar coordinates of each point to three decimal places.

Answers (1)

2021-02-12
Rec tan gular coordinates \(= ( x, y) = (-5, 2)\) Polar coordinates \(= (r, \theta)\) Then, formula for finding r and theta, is given by - \(r = \sqrt{x^2 + y^2}\)
\(r = \sqrt{(-5)^2 + (2)^2}\)
\(r = \sqrt{(25 + 4)}\)
\(r = \sqrt{29}\)
\(r = 5.385\) And, \(\theta = \tan^{-1} (\frac{y}{x})\)
\(\theta = \tan^{-1} (\frac{2}{-5})\)
\(\theta = tan^{-1} (\frac{2}{5}) [tan^{-1} (-x) = - tan^{-1} (x)]\)
\(\theta = -0.380\) radians Polar coordinates \(= (r, \theta) = (5.385, - 0.380)\)
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