convert the point from cartesian to polar coordinates. write your answer in radians. round to the nearest…

Explanation:

Step1: Calculate the value of (r)

Use the formula (r = \sqrt{x^{2}+y^{2}}). Given (x=\sqrt{3}) and (y = - 1), then (r=\sqrt{(\sqrt{3})^{2}+(-1)^{2}}=\sqrt{3 + 1}=\sqrt{4}=2).

Step2: Calculate the value of (\theta)

Use the formula (\tan\theta=\frac{y}{x}). Here, (\tan\theta=\frac{-1}{\sqrt{3}}). The point ((\sqrt{3},-1)) is in the fourth - quadrant. So (\theta=\arctan\left(-\frac{1}{\sqrt{3}}\right)+2\pi). Since (\arctan\left(\frac{1}{\sqrt{3}}\right)=\frac{\pi}{6}), then (\theta = 2\pi-\frac{\pi}{6}=\frac{12\pi-\pi}{6}=\frac{11\pi}{6}\approx5.76) (in radians, rounded to the nearest hundredth).

Answer:

The polar coordinates are ((2,5.76))