Question

Find all polar coordinates of point P where P =(5,pi/3)

Answer 1

@iPwnBunnies

Answer 2

(5, pi divided by 3 + nπ) or (-5, pi divided by 3 + nπ)

(5, pi divided by 3 + (2n + 1)π) or (-5, pi divided by 3 + 2nπ)

(5, pi divided by 3 + 2nπ) or (-5, pi divided by 3 + (2n + 1)π)

(5, pi divided by 3 + 2nπ) or (-5, pi divided by 3 + 2nπ)

Answer 3

Ok. It looks kinda confusing. Do you understand that 2pi radians makes a complete circle. And pi radians a half a circle?

Answer 4

yep i understand that

Answer 5

Ok. So if we have point (5, pi/3)
If we add any multiple of 2pi to the pi/3, it'll just go back to the same angle, right?

Answer 6

yah makes sense

Answer 7

Good, so for the first part, we can write it like this:
\[(5, \frac{\pi}{3} + 2 \pi n)\] Where 'n' can be any integer.

Answer 8

Alright, ya that eliminates 2 options :D

Answer 9

Yes! Now, for the next part.

Answer 10

(5, pi/3) is the same as (-5, pi/3 + pi)

Answer 11

It's the angle exactly opposite of pi/3. But since 'r' is negative, we trace it backwards, so it's the same point.

Answer 12

hmmm alright. ya i understand that

Answer 13

Ok, good. However, it can't be any multiple of pi. Because if we use pi/3 + 2pi, that'll be an angle similar to pi/3, which isn't what we want. We want every ODD integer, which we can write like this:
\[(5, \frac{\pi}{3}) = (-5,\frac{\pi}{3} + (2n + 1)\pi)\]
Where 'n' is any integer.

Answer 14

Thanks man! Do you have time for one more problem? It's my last one. I really appreciate your help

Answer 15

Ok.