The rectangular coordinates of a point are given. Find polar coordinates for the point.
-(100, -30) Round the polar coordinates to two decimal places, with θ in degrees.
A) (104.40, 16.70°)
B) (104.40, -106.70°)
C) (104.40, -16.70°)
D) (104.40, 106.70°)

Question

Quizplus · Accepted Answer

The polar coordinates (r, θ) can be found from the rectangular coordinates (x, y) using the formulas $r = \sqrt{x^2 + y^2}$ and $\theta = \tan^{-1}\left(\frac{y}{x}\right)$. For the point (100, -30), $r = \sqrt{100^2 + (-30)^2} = \sqrt{10000 + 900} = \sqrt{10900} \approx 104.40$. The angle $\theta = \tan^{-1}\left(\frac{-30}{100}\right) \approx -16.70^\circ$, because the point is in the fourth quadrant where angles are typically measured as negative from the positive x-axis.

The Rectangular Coordinates of a Point Are Given