Give the rectangular coordinates for the point.
-$\left( - 4,45 ^ { \circ } \right)$
A) $( 2 \sqrt { 2 } , 2 \sqrt { 2 } )$
B) $( - 2 \pi , - 2 \pi )$
C) $( - 2 \sqrt { 2 } , - 2 \sqrt { 2 } )$
D) $( - 2 \sqrt { 3 } , - 2 \sqrt { 3 } )$

Question

Quizplus · Accepted Answer

To convert polar coordinates $(r, \theta)$ to rectangular coordinates $(x, y)$, we use the formulas $x = r \cos(\theta)$ and $y = r \sin(\theta)$. Given $(r, \theta) = (-4, 45^\circ)$, we find $x = -4 \cos(45^\circ) = -4(\sqrt{2}/2) = -2\sqrt{2}$ and $y = -4 \sin(45^\circ) = -4(\sqrt{2}/2) = -2\sqrt{2}$, making the rectangular coordinates $(-2\sqrt{2}, -2\sqrt{2})$.

Give the Rectangular Coordinates for the Point (−4,45∘)\left( - 4,45 ^ { \circ } \right)(−4,45∘)

Give the Rectangular Coordinates for the Point $\left( - 4,45 ^ { \circ } \right)$