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Math Help - prove cojecture: what does this mean?

  1. #1
    Member sinewave85's Avatar
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    prove cojecture: what does this mean?

    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?
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  2. #2
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    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 \angle{OAB},\;\angle{OBC},\;and\;\angle{OCD}?

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