We have been given the rectangular coordinates (-4,4) and we have to find the polar coordinates of the points.
as we know that \(r = \sqrt(x^2 + y^2)\)
now as rectangular coordinates are (x, y) and polar coordinates are \((r, \theta)\).
\(r = \sqrt{(-4)^2 + 4^2}\)

\(r = \sqrt{16 + 16}\)

\(r = \sqrt{32}\)

\(r = 4\sqrt 2\) now as we know that \(\alpha = tan^−1 \frac{y}{x}\) \(a = tan^-1 \frac{4}{-4}\)

\(a = tan^-1 (-1)\)

\(a = - \frac{\pi}{4}\)

\(\theta = -\pi/4 + \pi = \frac{3\pi}{4}\)

\(\theta = \frac{3\pi}{4}\) now The required polar coordinate \(=(4\sqrt 2, 3\\frac{\pi}{4})\)

\(r = \sqrt{16 + 16}\)

\(r = \sqrt{32}\)

\(r = 4\sqrt 2\) now as we know that \(\alpha = tan^−1 \frac{y}{x}\) \(a = tan^-1 \frac{4}{-4}\)

\(a = tan^-1 (-1)\)

\(a = - \frac{\pi}{4}\)

\(\theta = -\pi/4 + \pi = \frac{3\pi}{4}\)

\(\theta = \frac{3\pi}{4}\) now The required polar coordinate \(=(4\sqrt 2, 3\\frac{\pi}{4})\)