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Find all the values of x in the interval [0,2π] that satisfy the equation: 8sin(2x)=8cos(x)

  • math -

    3 1/2+ 3/4 = xz\

  • math -

    ^ that's not the answer

  • math -

    8sin(2x)=8cos(x)
    8(2sinxcosx) - 8cosx = 0
    16sinxcosx - 8cosx = 0
    8cosx(2sinx - 1) = 0
    cosx = 0 or sinx = 1/2

    if cosx = 0, x = π/2 or x = 3π/2

    if sinx = 1/2, x = π/6 or 5π/6

    x = 0, π/6, 5π/6, 3π/2

  • math -

    I think you mean x = π/2, π/6, 5π/6, 3π/2... 0 shouldnt be included

  • you are correct - math -

    good catch anonymous.

    that was just a typo, notice I actually had the right answer in the solution part.

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