Question

find polar coordinates of the point that has rectangular coordinates (2, -4). write your answer using degrees, and round your coordinates to the nearest hundredth. polar coordinates: ( , °)

Explanation:

Step1: Calculate the value of \(r\)

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

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Step2: Calculate the value of \(\theta\)

Use the formula \(\tan\theta=\frac{y}{x}\), where \(x = 2\) and \(y = - 4\). So \(\tan\theta=\frac{-4}{2}=-2\).
Since the point \((2,-4)\) is in the fourth - quadrant, \(\theta=\arctan(-2)+360^{\circ}\).
Using a calculator, \(\arctan(-2)\approx - 63.43^{\circ}\), then \(\theta\approx - 63.43^{\circ}+360^{\circ}=296.57^{\circ}\)

Answer:

\((4.47,296.57^{\circ})\)