Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.
A)Rectangular coordinates: (-7.13,-1.02)
B)Rectangular coordinates: (-1.02,-7.13)
C)Rectangular coordinates: (-6.13,-1.02)
D)Rectangular coordinates: (-7.13,-0.02)
E)Rectangular coordinates: (-6.13,-0.02)

Question

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. ​  ​
A)Rectangular coordinates: (-7.13,-1.02) 
B)Rectangular coordinates: (-1.02,-7.13) 
C)Rectangular coordinates: (-6.13,-1.02) 
D)Rectangular coordinates: (-7.13,-0.02) 
E)Rectangular coordinates: (-6.13,-0.02)

Quizplus · Accepted Answer

To convert from polar to rectangular coordinates, we use the formulas $x=r\cos	heta$ and $y=r\sin	heta$. In this case, $r=8.02$ and $	heta=-227.08^\circ$ (since the given angle is measured counterclockwise from the positive $x$-axis and $	heta$ is measured clockwise from the positive $x$-axis in standard position). Plugging in to the formulas, we get $x=8.02\cos(-227.08^\circ)=-7.13$ and $y=8.02\sin(-227.08^\circ)=-1.02$, so the rectangular coordinates are $(-7.13,-1.02)$. Therefore, the answer is A.

Find the Rectangular Coordinates of the Point Given in Polar