A point in rectangular coordinates is given. Convert the point to polar coordinates. $( - 4,0 )$
A) Polar coordinates: $( 4,2 \pi )$
B) Polar coordinates: $\left( 4 , \frac { \pi } { 2 } \right)$
C) Polar coordinates: $( - 4,2 \pi )$
D) Polar coordinates: $( - 4 , \pi )$
E) Polar coordinates: $( 4 , \pi )$

Question

A point in rectangular coordinates is given. Convert the point to polar coordinates. $( - 4,0 )$ 
A) Polar coordinates: $( 4,2 \pi )$
B) Polar coordinates: $\left( 4 , \frac { \pi } { 2 } \right)$
C) Polar coordinates: $( - 4,2 \pi )$
D) Polar coordinates: $( - 4 , \pi )$
E) Polar coordinates: $( 4 , \pi )$

Quizplus · Accepted Answer

To convert rectangular coordinates to polar coordinates, we use the formulas: $r=\sqrt{x^2+y^2}$ and $	heta=	an^{-1} \left( \frac{y}{x} ight)$. In this case, $y=0$ and $x=-4$, so $r=\sqrt{(-4)^2+0^2}=4$ and $	heta=	an^{-1} \left( \frac{0}{-4} ight)=	an^{-1}(0)=0$ or $\pi$. Since the point lies on the negative x-axis, $	heta=\pi$. Thus, the polar coordinates are $(4,\pi)$, which matches choice E.

A Point in Rectangular Coordinates Is Given (−4,0)( - 4,0 )(−4,0)

A Point in Rectangular Coordinates Is Given $( - 4,0 )$