Give the rectangular coordinates for the point.
-$$\left( - 5,120 ^ { \circ } \right)$$
A) $\left( \frac { 5 } { 2 } , - \frac { 5 \sqrt { 3 } } { 2 } \right)$
B) $\left( - \frac { 5 } { 2 } , \frac { 5 \sqrt { 3 } } { 2 } \right)$
C) $\left( - \frac { 5 } { 2 } , - \frac { 5 \sqrt { 3 } } { 2 } \right)$
D) $\left( \frac { 5 } { 2 } , \frac { 5 \sqrt { 3 } } { 2 } \right)$

Question

Quizplus · Accepted Answer

To convert polar coordinates $(r, \theta)$ to rectangular coordinates $(x, y)$, we use the formulas $x = r \cos(\theta)$ and $y = r \sin(\theta)$. For $(-5, 120^\circ)$, $r = -5$ and $\theta = 120^\circ$. Thus, $x = -5 \cos(120^\circ) = -5 \left(-\frac{1}{2}\right) = \frac{5}{2}$ and $y = -5 \sin(120^\circ) = -5 \left(\frac{\sqrt{3}}{2}\right) = -\frac{5\sqrt{3}}{2}$, making the rectangular coordinates $\left(\frac{5}{2}, -\frac{5\sqrt{3}}{2}\right)$.

Give the Rectangular Coordinates for the Point (−5,120∘)\left( - 5,120 ^ { \circ } \right)(−5,120∘)

Give the Rectangular Coordinates for the Point $\left( - 5,120 ^ { \circ } \right)$