Question

convert the point from cartesian to polar coordinates. write your answer in radians. round to the nearest hundredth. (5, - 10)

Explanation:

Step1: Calculate the radius \(r\)

Use the formula \(r = \sqrt{x^{2}+y^{2}}\). Given \(x = 5\) and \(y=-10\), then \(r=\sqrt{5^{2}+(- 10)^{2}}=\sqrt{25 + 100}=\sqrt{125}=5\sqrt{5}\approx11.18\)

Step2: Calculate the angle \(\theta\)

Use the formula \(\tan\theta=\frac{y}{x}\). Here, \(\tan\theta=\frac{-10}{5}=-2\). Since the point \((5,-10)\) is in the fourth quadrant (\(x>0,y < 0\)), \(\theta=\arctan(-2)+2\pi\). \(\arctan(-2)\approx - 1.11\) radians, and \(\theta\approx-1.11 + 2\pi\approx5.17\) radians

Answer:

The polar coordinates are \((11.18,5.17)\)