Find the Cartesian coordinates of the given point.
-$$\left( 16 , - \frac { \pi } { 4 } \right)$$
A) $( 8 \sqrt { 3 } , - 8 )$
B) $( 8 \sqrt { 2 } , - 8 \sqrt { 2 } )$
C) $( - 16 \sqrt { 2 } , - 16 \sqrt { 2 } )$
D) $( - 8 \sqrt { 2 } , - 8 \sqrt { 2 } )$

Question

Quizplus · Accepted Answer

The given point is in polar coordinates $(r, \theta) = (16, -\frac{\pi}{4})$. To convert to Cartesian coordinates $(x, y)$, use $x = r \cos(\theta)$ and $y = r \sin(\theta)$. Here, $\cos(-\frac{\pi}{4}) = \sin(-\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$, so $x = 16 \cdot \frac{\sqrt{2}}{2} = 8\sqrt{2}$ and $y = 16 \cdot \frac{\sqrt{2}}{2} = 8\sqrt{2}$, but since it's in the 4th quadrant (negative angle), $y$ is negative, making the coordinates $(8\sqrt{2}, -8\sqrt{2})$.

Find the Cartesian Coordinates of the Given Point (16,−π4)\left( 16 , - \frac { \pi } { 4 } \right)(16,−4π​)

Find the Cartesian Coordinates of the Given Point $\left( 16 , - \frac { \pi } { 4 } \right)$