A. Find arctan(1) + arctan(2) + arctan(3) using a calculator. Make a conjecture about the exact value. Prove your conjecture using reference triangles.
Ok, so the exact value is 180 degrees (or pi rads), so I guess I can "conjecture" that the angles add up to a straight line? But that seems too easy -- all I am saying is that 180 degrees is, well, 180 degrees. I can prove that by drawing the triangles so that the three angles form a line?
B. Prove the conjecture from part A using trigonometric identities.
Well, tan(arctan(1) + arctan(2) + arctan(3)) = 0, and tan(180 degrees) = 0 -- does that prove the conjecture?