writing polar coordinates angles in different ranges

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The range of $\theta$ doesn't matter, as long as you cover a full circle. You have multiple choices

$$0\leq\theta<2\pi$$ $$-\pi\leq\theta<\pi$$ $$-2\pi\leq\theta<0$$

and so on. However, in all cases you can still use

$$\left(x,y\right)=\left(r\cos\theta,r\sin\theta\right)$$

EDIT: As for your edited question, you need to understand that if

$$\theta_{1}=\theta_{2}+2\pi$$

then both describe the same point. So find a $\theta$ that fits to this point, then add/subtract $2\pi$ to get into the desired domain.

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In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei

Updated on August 01, 2022

Comments

  • Катя
    Катя over 1 year

    What does it mean to write a polar coordinate with an angle in the range $-2\pi \le \theta < 0$?

    Say i have $(r,\theta)$ in the $0 \le \theta < 2\pi$, how i would i translate that polar coordinate into the range $-2\pi \le \theta < 0$?

    It all seems to me, like its just a matter of reference point, why does the range matter if this is just a point and not a vector?

    Here is the particular dilemmer i am dealing with!

  • Катя
    Катя almost 6 years
    so, if i were to pick a polar coordinate and change the range I would not have to change how i refer to the polar coordinate? @eranreches
  • eranreches
    eranreches almost 6 years
    @studiousstudent You don't have to change the way you refer to the coordinates, because this coordinate choice still covers all the plane.
  • Катя
    Катя almost 6 years
    perhaps i was not clear in the way i stated my question, but i reposted the question i was struggling with. Do you mind looking over it and explaining to me why the angle changes. I understand that it is just the angle of $7\pi/4$ reflected back into first quandrant, which in the case is saying the same exact thing as $\pi/ 4$ but why this odd process?
  • eranreches
    eranreches almost 6 years
    @studiousstudent I edited my answer.
  • Катя
    Катя almost 6 years
    ah...now i can see what they meant, they are delibrately, just substracting $2\pi$ from the given range thus all you need to do to accommodate for that change is do the same with the given coordinates. Thanks!!