Question

Find all polar coordinates of point P = (9, 75\(^o\)).

Answer 1

@freckles

Answer 2

so I guess you are given no restrictions

Answer 3

Nope

Answer 4

\[(r, \theta)=(r, \theta+360^o n) \text{ where } n \text{ is an integer } \\ (r, \theta)=(-r, \theta+(2n+1) 180^o) \text{ where } n \text{ is an integer }\]
on and of course our theta is in degrees

Answer 5

those are two ways to write (r, theta)

Answer 6

the first way is true because you can keep making a full rotation after the theta you found and still land on the same spot

Answer 7

the second way is true
and the problem you did before is an example of it

Answer 8

\[(4 \sqrt{2}, 315^o)=(-4 \sqrt{2}, 315^o+(2 \cdot (-1)+1)180^o) \text{ where } \\ n=-1 \text{ for our last problem } \\ \text{ ... } (-4 \sqrt{2},315^o-180^o)=(-4 \sqrt{2},135^o)\]

Answer 9

oops I have to go

Answer 10

Okay, thanks for the help :)

Answer 11

To me, I interpret the problem in different way :)

Answer 12

Hence your point \(A(9, 75^0)\)

Answer 13

If you go to this point and take the distance in negative direction, you have A back

Answer 14

Another point is negative angle, negative lenght

Answer 15

Hmmm... would that be all if I used that way?

Answer 16

(-9,-105)

Answer 17

How do you get a negative angle?

Answer 18

And then from those points, if you generalize them by + 2npi to the angle, you have the whole answer

Answer 19

from 0 , go counterclockwise an 105 degree

Answer 20

Would I subtract 180 from the original angle given?

Answer 21

Oh, okay :)

Answer 22

I don't know why, it does not allow me to use draw box, hehehe.. but I believe you get the idea