What does the trig book mean? Need help with trig

[Jurrasic]

Can anyone tell me what the trig book is trying to tell me? Don't know what they mean by this?
It says Finding other polar coordinate of a given point.
Plot the point P with polar coordinates (3, pi/6) and find other polar coordinates for (r , theta) of this same point for which :
there are 3 different things that they want you to do, they are:
r>0 , 2pi< or equal to theta < 4pi
r<0 , 0< or equal to theta < 2pi
and then r>0 , -2pi< or equal to theta < 0

The last part above confuses me because, I was wondering a few things:
in the book to get the solution, they say to add like pi, or 2pi or sometimes to subtract pi, how do you know when you are supposed to add or subtract however much pi?

like for the first one you add 2pi to get (3, 13pi/6) that's the answer , how do you know to add 2pi, why not 3 pi? 3 pi is still between 2pi< or equal to theta < 4pi

in the last one they subtracted 2pi? why did they? OK so There must be then, more rules that they aren't telling you on how you know to add/subtract how much more pi to the theta in the point P?

 

[QuarkCharmer]

If I have some polar coordinate (r, θ), there are many possibilities. I could have a θ that is pointing in the opposite direction with a negative radius. I could also have any number of coterminal angles to θ.

The adding/subtracting 2π is simply indicating a coterminal angle.

For instance, I can say π ± 2kπ, where k is any whole number, and the resulting angle will always be coterminal with π.

There is literally an infinite number of solutions to these problems.

like for the first one you add 2pi to get (3, 13pi/6) that's the answer , how do you know to add 2pi, why not 3 pi? 3 pi is still between 2pi< or equal to theta < 4pi

They knew to add 2π because one revolution about the circle (sweeping 360deg/2πrad) takes 2π.

 

[Jurrasic]

If I have some polar coordinate (r, θ), there are many possibilities. I could have a θ that is pointing in the opposite direction with a negative radius. I could also have any number of coterminal angles to θ.

So can you relate that idea to why they add different amounts of pi to get the solution?

 

[Jurrasic]

If I have some polar coordinate (r, θ), there are many possibilities. I could have a θ that is pointing in the opposite direction with a negative radius. I could also have any number of coterminal angles to θ.

The adding/subtracting 2π is simply indicating a coterminal angle.

For instance, I can say π ± 2kπ, where k is any whole number, and the resulting angle will always be coterminal with π.

There is literally an infinite number of solutions to these problems.
They knew to add 2π because one revolution about the circle (sweeping 360deg/2πrad) takes 2π.

Sorry did not see that what you just wrote. Thanks that is really helpful. Many thanks :)

 

[QuarkCharmer]

No problem.