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March 29, 2017

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Solve 3cos2x - 7cosx = 0, when 0<=x<=360

And also, find the exact values for x when 0<=x<=360 if 3tan^2x=1


Thankyou!

  • Maths - trig - ,

    have you come across
    cos 2x = 2cos^2 x - 1 ?
    let's sub it.
    3cos 2x - 7cosx = 0
    3(2cos^2 x - 1) - 7cosx = 0
    6cos^2x - 7cosx - 3 = 0
    (2cosx-3)(3cosx+1) = 0

    cosx = 3/2 , which is not possible,
    or
    cosx = -1/3
    so x must be in quadrants II or III
    angle in standard position is 7.53 , then
    x = 180-70.53 = 109.47°
    or
    x = 180+70.53 = 250.53

  • 2nd part Maths - trig - ,

    3tan^2 = 1
    tan^2x = 1/3
    tanx = ± 1/√3

    x = 30°, 150°, 210° or 330°

  • ìàòåìàòèêà - ,

    3cos2x+7cosx+3=0

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