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√(3))`

Explanation:

Given the point in polar coordinate:

`\left(5,-(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(-(2\pi)/(3)\right),5\sin\left(-(2\pi)/(3)\right)\right) \\ =\left(5*-(1)/(2),5*-(√(3))/(2)\right) \\ =(-2.5,-2.5√(3)) \end{gathered}`

The Cartesian coordinates are:

`(-2.5,-2.5√(3))`