# Which of the following polar coordinate pairs does not represent the point with rectangular coordinates (-2,-2)?(A)(2sqrt2.−135°)(B)(2sqrt2. 225°)

Which of the following polar coordinate pairs does not represent the point with rectangular coordinates (-2,-2)?
(A)$\left(2\sqrt{2}.-135°\right)$
(B)$\left(2\sqrt{2}.225°\right)$
(C)$\left(-2\sqrt{2}.-315°\right)$
(D)$\left(-2\sqrt{2}.45°\right)$
(E)$\left(-2\sqrt{2}.135°\right)$
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Nathanael Webber

A polar coordinate $\left(r;\theta \right)$ is given, then $\left(x;y\right)=\left(r×\mathrm{cos}\theta ;r×\mathrm{sin}\theta \right)$

A) $\left(2\sqrt{2}\mathrm{cos}\left(-{135}^{\circ }\right),2\sqrt{2}\mathrm{sin}\left(-{135}^{\circ }\right)\right)=\left(2\sqrt{2}×-\frac{\sqrt{2}}{2};2\sqrt{2}×-\frac{\sqrt{2}}{2}\right)=\left(-2;-2\right)$

B) $\left(2\sqrt{2}\mathrm{cos}{225}^{\circ },2\sqrt{2}\mathrm{sin}{225}^{\circ }\right)=\left(2\sqrt{2}×-\frac{\sqrt{2}}{2};2\sqrt{2}×-\frac{\sqrt{2}}{2}\right)=\left(-2;-2\right)$

C) $\left(-2\sqrt{2}\mathrm{cos}\left(-{315}^{\circ }\right),-2\sqrt{2}\mathrm{sin}\left(-{315}^{\circ }\right)\right)=\left(-2\sqrt{2}×\frac{\sqrt{2}}{2};-2\sqrt{2}×\frac{\sqrt{2}}{2}\right)=\left(-2;-2\right)$

D) $\left(-2\sqrt{2}\mathrm{cos}{45}^{\circ },-2\sqrt{2}\mathrm{sin}{45}^{\circ }\right)=\left(-2\sqrt{2}×\frac{\sqrt{2}}{2};-2\sqrt{2}×\frac{\sqrt{2}}{2}\right)=\left(-2;-2\right)$

E) $\left(-2\sqrt{2}\mathrm{cos}{135}^{\circ },-2\sqrt{2}\mathrm{sin}{135}^{\circ }\right)=\left(-2\sqrt{2}×-\frac{\sqrt{2}}{2};-2\sqrt{2}×\frac{\sqrt{2}}{2}\right)=\left(2;-2\right)$

Choice (E) does not represent $\left(-2;-2\right)$.