Give the rectangular coordinates for the point.
-(10, $\left. 225 ^ { \circ } \right)$
A) $( - 5 \sqrt { 2 } , - 5 \sqrt { 2 } )$
B) $( 5 \sqrt { 2 } , 5 )$
C) $( 5,5 \sqrt { 2 } )$
D) $( - 5 \sqrt { 2 } , - 5 )$

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 the point $(10, 225^\circ)$, we have $r = 10$ and $\theta = 225^\circ$. Since $\cos(225^\circ) = -\frac{\sqrt{2}}{2}$ and $\sin(225^\circ) = -\frac{\sqrt{2}}{2}$, we get $x = 10 \times -\frac{\sqrt{2}}{2} = -5\sqrt{2}$ and $y = 10 \times -\frac{\sqrt{2}}{2} = -5\sqrt{2}$, making the rectangular coordinates $(-5\sqrt{2}, -5\sqrt{2})$.

Give the Rectangular Coordinates for the Point 225∘)\left. 225 ^ { \circ } \right)225∘)

Give the Rectangular Coordinates for the Point $\left. 225 ^ { \circ } \right)$