Question

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

Answer 1

Step 1: Write out the coordinates of the rectangle given

$(-4,2)$

Step 2: Write out the expression of the polar coordinates

The polar coordinates is given as

$\begin{gathered} (r,\theta) \\ r=\sqrt[]{x^2+y^2)} \\ \tan \theta=\frac{y}{x} \end{gathered}$

Step 3: Solve for the polar coordinates using the formula

$\begin{gathered} x=-4;y=2 \\ r=\sqrt[]{(-4)^2+2^2} \\ r=\sqrt[]{16+4} \\ r=\sqrt[]{20} \end{gathered}$$\begin{gathered} r=4.472 \\ r=4.47(\text{nearest hundredth)} \end{gathered}$$\begin{gathered} \tan \theta=\frac{2}{-4} \\ \tan \theta=-0.5 \\ \theta=(-26.565) \end{gathered}$

Since tan is negative in the second quadrant, the value of the angle will be

$\begin{gathered} \theta=180-26.565 \\ \theta=153.45 \end{gathered}$

Hence, the polar coordinates is (4.47, 153.45°)