Question

What would be two sets of polar coordinates that can be used to plot the given point? Pic attached, help is appreciated <3

Answer 1

this point can either be plotted with the positive (counter-clockwise direction) or the negative (clockwise direction).

format of a point is: \[re^(i \theta)\]
the format of the other would be: \[re^(i(2\pi - \theta))\]

Answer 2

Is there an exact answer to this or there's a variety answers that can be correct?

Answer 3

There is an infinite amoun of answers that could be given, unless some limit on theta is given since \[ \theta + 2k \pi \] will return the same reference angle. So, the answer would be \[ (r, \theta) = (\frac{5}{2}, -\frac{\pi}{3}+2k\pi) \]

where k is any integer you wish.

Answer 4

One more clarification, you could also have a negative radius to obtain:
\[ (\frac{-3}{2}, \frac{2 \pi}{3} + 2k\pi) \]

Answer 5

Thanks! Can I also get help on this one and that's it?

Answer 6

It has a radius of three right and an angle of either 3pi/2 or -pi/2 then you can add your 2kpi.

OR

-3 radius and an angle of pi/2

Answer 7

Okay, thank you so much!