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Finding theta in the correct quadrant

I can never seem to work out the correct quadrant for which theta should be.

Say in plane polar coordinates x = -3 and y = 2.

Then find r and theta.

I can find r to be root 13 and tan(theta) = -2/3

When i inverse tan I get -.588 when it should be 2.55.

Can someone explain how to find out how I should know this ? I didn't have a any experience with the unit circle before coming to Uni.
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Mark85
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Original post by Voltozonic
I can never seem to work out the correct quadrant for which theta should be.

Say in plane polar coordinates x = -3 and y = 2.

Then find r and theta.

I can find r to be root 13 and tan(theta) = -2/3

When i inverse tan I get -.588 when it should be 2.55.

Can someone explain how to find out how I should know this ? I didn't have a any experience with the unit circle before coming to Uni.


If I told you that without thinking about any formulas or methods for a moment; what you are actually trying to do is find the angle between the positive x-axis and the line joining the origin to the point (-3,2) would that help?

Clearly such an angle is between pi/2 and pi radians or is in the second quandrant if that is how you want to put it.

Obviously, the angles -.588 and 2.55 are the same (at least taken to 2d.p.)
so both answers are 'right'.

I am guessing your question is wanting you to write the principal value of the argument. This will depend on your conventions but is normally defined as either: an angle between -pi and pi or an angle between 0 and 2pi. In this case, it doesn't matter, since the angle is less than pi so 2.55 would be the correct answer.

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