QuestionFind the polar coordinates, $0 \leq \theta<2 \pi$ and $r \geq 0$, of the point given in Cartesian coordinates. A) $\left(2, \frac{5 \pi}{4}\right)$ B) $\left(2, \frac{7 \pi}{4}\right)$ $$(\sqrt{2},-\sqrt{2})$$ C) $\left(\sqrt{2}, \frac{7 \pi}{4}\right)$ D) $\left(4, \frac{5 \pi}{4}\right)$

Studdy Solution
Match the calculated polar coordinates $(r, \theta) = (2, \frac{7\pi}{4})$ with the given options:
A) $(2, \frac{5\pi}{4})$ B) $(2, \frac{7\pi}{4})$ C) $(\sqrt{2}, \frac{7\pi}{4})$ D) $(4, \frac{5\pi}{4})$
The correct match is option B: $(2, \frac{7\pi}{4})$.
The polar coordinates of the point $(\sqrt{2}, -\sqrt{2})$ are:
$$\boxed{(2, \frac{7\pi}{4})}$$