If the Cartesian coordinate of any point are \( (-1,-1) \) then its polar coordinates are (A) \( \left(\sqrt{2}, \frac{-3 \pi}{4}\right) \) (B) \( \left(\sqrt{2}, \frac{3 \pi}{4}\right) \) (C) \( \left(\sqrt{2}, \frac{-5 \pi}{4}\right) \) (D) \( \left(\sqrt{2}, \frac{5 \pi}{4}\right) \)
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Which of the following pairs of polar coordinates can represent the point $(x, y)=(1,-1)$ in cartesian coordinates? $$ I:\left(\sqrt{2},-\frac{\pi}{4}\right) \quad I I:\left(-\sqrt{2}, \frac{\pi}{4}\right) \quad I I:\left(-\sqrt{2}, \frac{3 \pi}{4}\right) \quad I V:\left(\sqrt{2}, \frac{5 \pi}{4}\right) \quad V:\left(\sqrt{2}, \frac{7 \pi}{4}\right) $$ A) $I, I I I, I V$ B) $I, I I I, V$ c) $I, I V, V$ D) $I, I I, I I I$ E) $I, I V, V$
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The Cartesian coordinates of the point whose polar coordinates are $\left(4, \frac{\pi}{3}\right)$, are (a) $(2 \sqrt{3}, 2)$ (b) $(2,2 \sqrt{3})$ (c) $(2,-2 \sqrt{2})$ (d) $(2,2 \sqrt{2})$
Plot the point whose polar coordinates are given. Then find the Cartesian coordinates of the point. $$(\mathrm{a})(1, \pi) \quad \text { (b) }(2,-2 \pi / 3) \quad \text { (c) }(-2,3 \pi / 4)$$
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