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determine the general solution...2.sin(2x+30)=tan 135

  • mathematics -

    The 135 suggests that you are working in degrees, so

    2 sin(2x+30) = tan 135°
    2sin(2x+30) = -1
    sin(2x + 30) = -1/2
    sine is negative in III and IV
    so 2x+30 = 210 or 2x+30 = 330
    2x = 180 or 2x = 300
    x = 90 or x = 150
    The period of sin(2x+30) is 360°/2 or 180°

    so general solutions are:
    90° + 180k° or 150° + 180k°

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