Question

Topic : Multiple Representations of points

Answer 1

Answer:

Hmm, want piña colada and Jar Jar Binks cookies? just go to India.

Answer 2

Answer:

See below directions.

Step-by-step explanation:

The condition $-2\pi$ 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 $\left(3,\,-\frac{3\pi}{4}\right)$.  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 $\frac{3\pi}{4}$.

Now, go again, starting at the origin, only this time, go 3 units right, then turn through an angle of $-\frac{3\pi}{4}+2\pi=\frac{5\pi}{4}$.  In other words, you turn one whole revolution in addition to the $-\frac{3\pi}{4}$ angle.  Your point can now be described by $\left(3,\,\frac{5\pi}{4}\right)$.

Another description can be found by rotating in the opposite direction, so an angle of $\frac{3\pi}{4}$ and backing up 3 units -- specify a "radius" of -3.  The point is then $\left(-3,\,\frac{3\pi}{4}\right)$.

You can also try subtracting one revolution $(2\pi)$ from the angle, but be careful not to let the angle go outside the interval  $-2\pi$.

The changes you can try are:  

add $2\pi$ to the angle, leave r alone

subtract $2\pi$ to the angle, leave r alone

add/subtract $\pi$ (half a revolution) to the angle, make r the opposite.