Answer:
See below directions.
Step-by-step explanation:
The condition [tex]-2\pi<\theta<2\pi[/tex] means you can get to the point by rotating no more than one revolution in either the positive or negative direction.
See the attached image to see the point [tex]\left(3,\,-\frac{3\pi}{4}\right)[/tex]. Think about how you get to that point: start at the origin, go right (along the positive x-axis) 3 units, then turn in the negative direction (to your right!) through an angle of [tex]\frac{3\pi}{4}[/tex].
Now, go again, starting at the origin, only this time, go 3 units right, then turn through an angle of [tex]-\frac{3\pi}{4}+2\pi=\frac{5\pi}{4}[/tex]. In other words, you turn one whole revolution in addition to the [tex]-\frac{3\pi}{4}[/tex] angle. Your point can now be described by [tex]\left(3,\,\frac{5\pi}{4}\right)[/tex].
Another description can be found by rotating in the opposite direction, so an angle of [tex]\frac{3\pi}{4}[/tex] and backing up 3 units -- specify a "radius" of -3. The point is then [tex]\left(-3,\,\frac{3\pi}{4}\right)[/tex].
You can also try subtracting one revolution [tex](2\pi)[/tex] from the angle, but be careful not to let the angle go outside the interval [tex]-2\pi<\theta<2\pi[/tex].
The changes you can try are:
add [tex]2\pi[/tex] to the angle, leave r alone
subtract [tex]2\pi[/tex] to the angle, leave r alone
add/subtract [tex]\pi[/tex] (half a revolution) to the angle, make r the opposite.
