Convert a Point from Polar to Rectangular Coordinates
-$$\left( 3 , - 135 ^ { \circ } \right)$$
A) $\left( \frac { - 3 \sqrt { 2 } } { 2 } , \frac { - 3 \sqrt { 2 } } { 2 } \right)$
B) $\left( \frac { - 3 \sqrt { 2 } } { 2 } , \frac { 3 \sqrt { 2 } } { 2 } \right)$
C) $\left( \frac { 3 \sqrt { 2 } } { 2 } , \frac { 3 \sqrt { 2 } } { 2 } \right)$
D) $\left( \frac { 3 \sqrt { 2 } } { 2 } , \frac { - 3 \sqrt { 2 } } { 2 } \right)$

Question

Quizplus · Accepted Answer

To convert from polar to rectangular coordinates, use the formulas $x = r \cos(\theta)$ and $y = r \sin(\theta)$. For $r = 3$ and $\theta = -135^\circ$, $\cos(-135^\circ) = \sin(-135^\circ) = -\frac{\sqrt{2}}{2}$. Thus, $x = 3 \times -\frac{\sqrt{2}}{2} = -\frac{3\sqrt{2}}{2}$ and $y = 3 \times -\frac{\sqrt{2}}{2} = -\frac{3\sqrt{2}}{2}$, making the coordinates $\left( -\frac{3\sqrt{2}}{2}, -\frac{3\sqrt{2}}{2} \right)$.

Convert a Point from Polar to Rectangular Coordinates - (3,−135∘)\left( 3 , - 135 ^ { \circ } \right)(3,−135∘)

Convert a Point from Polar to Rectangular Coordinates
- $\left( 3 , - 135 ^ { \circ } \right)$