Rectangular to Polar Coordinates: Remembering how to solve for theta

[BlueKai]

Can someone help me figure out how to get theta that highlighted in blue. I can't remember its been a while. I understand that tan(theta)= squareRoot(3) is positive in quadrants 1 and 3.

 

[Ishuda]

Can someone help me figure out how to get theta that highlighted in blue. I can't remember its been a while. I understand that tan(theta)= squareRoot(3) is positive in quadrants 1 and 3.
View attachment 5217

If you understand that tan(theta)= squareRoot(3) is positive in quadrants 1 and 3, then either x and y are both positive or x and y are both negative. If x and y are both positive then the angle is in the first quadrant, i.e. \(\displaystyle \theta=\tfrac{\pi}{3}\). If x and y are both negative then the angle is in the third quadrant, i.e. \(\displaystyle \theta=\tfrac{4\, \pi}{3}\).