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Half Angle Application

  1. Sep 28, 2010 #1
    1. The problem statement, all variables and given/known data

    find tan(theta) if sin (theta/2) = 3/5

    2. Relevant equations
    sin(theta/2) = sqrt[(1-cosx)/2]

    3. The attempt at a solution

    my attempt:

    first since we know the half angle formula for sin, let sqrt[(1-cosx)/2] = 3/5
    simplifying the equation, we get that cos(Theta) = 7/25 which is adjacent/hypothenus.
    using this, we can calculate the value of opposite using pythagoras theorum. which is 24 in this case. since tan = sin/cos and sin = 24/25 and cos = 7/25
    tan(Theta) = sin/cos which is 7/24

    is this the most correct approach to take from what the question is asking?
    please i would like to know if this will earn me full marks on a test or exam.

  2. jcsd
  3. Sep 28, 2010 #2
    very close, redo this step: "since tan = sin/cos and sin = 24/25 and cos = 7/25"

    Or just use tan = opp/adj
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