Question

Convert the following point from polar to Cartesian coordinates. Write the exact answer as an ordered pair. Do not round.(s. - 2)5.2.3

Answer 1

Answer::

$(-2.5,-2.5\sqrt{3})$

Explanation:

Given the point in polar coordinate:

$\left(5,-\frac{2\pi}{3}\right)$

To convert to Cartesian coordinates, use the formula below:

$(x,y)=(r\cos\theta,r\sin\theta)$

Thus:

$\begin{gathered} (x,y)=\left(5\cos\left(-\frac{2\pi}{3}\right),5\sin\left(-\frac{2\pi}{3}\right)\right) \\ =\left(5\times-\frac{1}{2},5\times-\frac{\sqrt{3}}{2}\right) \\ =(-2.5,-2.5\sqrt{3}) \end{gathered}$

The Cartesian coordinates are:

$(-2.5,-2.5\sqrt{3})$