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?

B) No, that does not prove the conjecture. Use your formula for the tangent of a sum of angles.

A) REALLY BIG HINT:

On a set of x-y coordinate axes, spot the following points:

A: (1,0)
B: (1,1)
C: (-1,3)
D: (-10,0)

Draw Line segments from the Origin (O) to each of these four points.
What are the lengths of these line segments?

Draw a line segment between A and B
Draw a line segment between B and C
Draw a line segment between C and D
What are the lengths of these line segments?

What can you say about the measure of ?

What can you say about the three angles at the origin? What are their tangents?