Use a graphing utility to find one set of polar coordinates for the point given in rectangular coordinates,r 0.Round your answers to three decimal places. $( 3 , - 2 )$
A)Polar coordinates: $( \sqrt { 2 } , - 0.588 )$
B)Polar coordinates: $( \sqrt { 1 } , - 0.588 )$
C)Polar coordinates: $( \sqrt { 13 } , - 0.588 )$
D)Polar coordinates: $( \sqrt { 13 } , 0.588 )$
E)Polar coordinates: $( \sqrt { 3 } , - 0.588 )$

Question

Use a graphing utility to find one set of polar coordinates for the point given in rectangular coordinates,r > 0.Round your answers to three decimal places.​ $( 3 , - 2 )$ ​
A)Polar coordinates: $( \sqrt { 2 } , - 0.588 )$
B)Polar coordinates: $( \sqrt { 1 } , - 0.588 )$
C)Polar coordinates: $( \sqrt { 13 } , - 0.588 )$
D)Polar coordinates: $( \sqrt { 13 } , 0.588 )$
E)Polar coordinates: $( \sqrt { 3 } , - 0.588 )$

Quizplus · Accepted Answer

To convert from rectangular coordinates $(x, y)$ to polar coordinates $(r, \theta)$, we use the formulas $r = \sqrt{x^2 + y^2}$ and $\theta = \arctan\left(\frac{y}{x}\right)$. For the point $(3, -2)$, $r = \sqrt{3^2 + (-2)^2} = \sqrt{9 + 4} = \sqrt{13}$. The angle $\theta$ in radians is $\arctan\left(\frac{-2}{3}\right)$, which is approximately $-0.588$. Therefore, the correct polar coordinates are $(\sqrt{13}, -0.588)$.

Use a Graphing Utility to Find One Set of Polar (3,−2)( 3 , - 2 )(3,−2)

Use a Graphing Utility to Find One Set of Polar $( 3 , - 2 )$