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 \(= (r, \theta) = (5.385, - 0.380)\)

\(r = \sqrt{(-5)^2 + (2)^2}\)

\(r = \sqrt{(25 + 4)}\)

\(r = \sqrt{29}\)

\(r = 5.385\) 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 \(= (r, \theta) = (5.385, - 0.380)\)