Basic trig question for physics

[laminar]

I have to calculate the phase constant for a mass and spring system for simple harmonic motion. If I find that phi equals the arctan of some negative over another negative number, do I have to add pi to the answer for it to be in quadrant III?

I know this is more of a precalculus question but I don't know if the rules are different for physics.

 

[courtrigrad]

yes, you have to add $$\pi$$.

 

[kyle8921]

In this case, you do not need to add pi to the answer for it to be in quadrant III. The arctan function will automatically return an angle in the correct quadrant based on the signs of the input numbers. In physics, we often use arctan or inverse tangent to find angles in a right triangle or to calculate phase shifts in simple harmonic motion. As long as you input the correct signs for your values, the result will be in the correct quadrant without needing to add or subtract pi. It is important to pay attention to the signs and use the appropriate quadrant for your calculations.