Tech: Polar Coordinates
-$( - 3 , - 6 )$ Express both $\mathrm { r }$ and $\theta$ to two decimal places.
A) $( 6.71 , - 2.03 )$
B) $( 6.71 , + 2.03 )$
C) $( 6.71 , - 1.11 )$
D) $( 6.71,1.11 )$

Question

Quizplus · Accepted Answer

The polar coordinates $r$ and $\theta$ can be found using the formulas $r = \sqrt{x^2 + y^2}$ and $\theta = \arctan\left(\frac{y}{x}\right)$. For $(-3, -6)$, $r = \sqrt{(-3)^2 + (-6)^2} = \sqrt{9 + 36} = \sqrt{45} \approx 6.71$. The angle $\theta$ in radians for the point in the third quadrant (where both $x$ and $y$ are negative) is $\arctan\left(\frac{-6}{-3}\right) + \pi = \arctan(2) + \pi \approx -1.11 + \pi \approx 2.03$.

Tech: Polar Coordinates - (−3,−6)( - 3 , - 6 )(−3,−6)

Tech: Polar Coordinates
- $( - 3 , - 6 )$