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Math Help - Solving Trigonometric Equations

  1. #1
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    Solving Trigonometric Equations

    Let f(x) = sin2x and g(x) = sin(0.5x).

    Consider the equation f(x) = g(x).
    Find the number of solutions to this equation, for 0 less than or equal to x less than or equal to 3pi/2.

    I know there are four solutions from graphing by hand and that I can determine the solutions using a graphing calculator. BUT how do I determine the solutions by hand?
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  2. #2
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    Let f(x) = sin2x and g(x) = sin(0.5x). And f(x) = g(x)
    Then
    sin(2x) = sin(0.5x)
    sin(2x) - sin(x/2) = 0....(1)
    Using
    sinC - sinD = 2cos[(C+D)/2]sin[(C-D)/2]
    simplify eq(1) and solve foe x.
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