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Although V(x) was -0.59, I noticed you did not use the negative sign in computing the angle-just the units. Would you please explain this? Thank you

Hi dorfte, good question. This has to do with my personal preference about calculating angles. When calculating angles with positive numbers, you'll always get an acute (less than 90 degrees) angle. By drawing a picture I figure out where the acute angle will be, then plug positive numbers into the inverse trig. function.

If you were to use -0.59 (with the negative), this would still be correct, but you'd have to know how to interpret the answer of -84 degrees. Your calculator knows nothing about the physics problem, and gives the smallest possible answer, which in this case, for tangent, is the angle of -84 degrees which is in the fourth quadrant (below pos. x-axis). You'd have to reinterpret this, and know that the magnitude of this answer (84 degrees) is the size of the angle above the negative x-axis as shown in the video.

Hope this helps!