Question

I need help with this practice problem solving from the trig section in my ACT prep guide

Answer 1

Step 1

Find the polar coordinates of the rectangular coordinates

`(-\sqrt[]{3},1)`

To convert from the cartesian coordinates (x,y) to polar coordinates (r,θ), we use the following equation.

`r^2=x^2+y^2`
`\theta=arc\tan ((y)/(x))`

Step 2

We have;

`(x,y)=(-\sqrt[]{3},1)`
`\begin{gathered} r^2=(-\sqrt[]{3})^2+1^2 \\ r^2=3+1 \\ r=\sqrt[]{4} \\ r=2 \\ \end{gathered}`
`\begin{gathered} \theta=arc\tan ((y)/(x)) \\ \theta=arc\tan (\frac{1}{-\sqrt[]{3}}) \\ \theta=\arctan (\frac{1}{-\sqrt[]{3}}*\frac{\sqrt[]{3}}{\sqrt[]{3}}) \\ \theta=\arctan \frac{\sqrt[]{3}}{-3} \\ \theta=-(\pi)/(6)+\pi \\ \theta=(5)/(6)\pi \end{gathered}`

The answer therefore is;

`(2,(5\pi)/(6))`