how do you solve 12cos^2x=3?

and in the interval [0,2pie)

Comments

  • divide both sides by 12.

    cos^2x = 3/12

    cos^2x = 1/4

    take the square root of both sides.

    cosx = 1/2

    For what value of x is cos(x) = 1/2? If you know the unit circle, you'll know this is pi/3.

    Or in other words...

    arccos(1/2) = pi/3.

    There is another solution in the fourth quadrant as well, 5pi/3.

  • 12cos^2 x=3

    cos^2 x = 3/12 = 1/4

    cos x = +/- 1/2

    either x = cos^-1 ( 1/2 ) = pi/3 or 5pi/3

    or x= cos^-1 ( -1/2) = 2pi/3 or 4pi/3

  • cos^2x=1/4

    cosx=1/2

    x=pi/3

    x=5pi/3

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