Question

Topic : Multiple Representations of points

PLEASE HELP ME, am having a hard time with these questions

Answer 1

See below directions.

Explanation:

The condition
`-2\pi<\theta<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,\,-(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
`(3\pi)/(4)`.

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

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

Answer 2

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