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Math Help - Trigo qn

  1. #1
    Member maybeline9216's Avatar
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    Trigo qn

    Given that A is measured in radians, find all the values of A between 0 and 5 for which 5sin(2A+3) + 3cos(2A+3)=0
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  2. #2
    MHF Contributor
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    Quote Originally Posted by maybeline9216 View Post
    Given that A is measured in radians, find all the values of A between 0 and 5 for which 5sin(2A+3) + 3cos(2A+3)=0
    Let X = (2A +3)
    So,
    5sinX +3cosX = 0
    5sinX = -3cosX
    sinX /cosX = -3/5
    tanX = -3/5 ----------negative tan value, so X is in the 2nd or 4th quadrants

    X = arctan(-3/5) = -0.5404195 radian

    In the 2nd quadrant,
    X = pi -0.5404195 = 2.6012 rad
    2A +3 = 2.6012
    A = (2.6012 -3) /2 = -0.1994 rad less than 0, so not counted.

    In the 4th quadrant,
    X = 2pi -0.5404195 = 5.7428 rad
    2A +3 = 5.7428
    A = (5.7428 -3) /2 = 1.3714 rad -------one counted.

    Now, the period of the tangent function is pi.
    Meaning, for every pi radians, the X here will repeat having tangent value of -0.5404195.

    So, in the 2nd quadrant, after one revolution,
    X = 3pi -0.5404195 = 8.8844 rad
    A = (8.8844 -3) /2 = 2.9422 rad ------two counted.

    In the next 4th quadrant,
    X = 4pi -0.5404195 = 12.0260
    A = (12.0260 -3)/2 = 4.513 rad --------3 counted.

    In the next 2nd quadrant again,
    X = 5pi -0.5404195 = 15.1675 rad
    A = (15.1675 -3) /2 = 6.0838 rad ------more than 5.0, so not counted anymore.

    Therefore, A = 1.3714, 2.9422 and 4.513 radians. ----------answer.
    Last edited by ticbol; October 9th 2008 at 04:34 AM.
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