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trig

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determine an exact expression for the trigonometric function sin(13pi/12).

  • trig -

    note that 13pi/12 is also 195 degrees, which can be expressed as difference of two angles, 240 - 45:
    sin(13pi/12) = sin(195) = sin(240-45)
    *expanding this,
    sin(240)cos(45)-cos(240)sin(45)
    (-sqrt(3)/2)(sqrt(2)/2)-(-1/2)(sqrt(2)/2)
    (-sqrt(6)/4)+(sqrt(2)/4)
    therefore:
    {[sqrt(2)-sqrt(6)]/4}

    so there,, :)

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