find the exact solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list.)?
Find the exact solutions of the equation (4 \sin(4x) = -8 \sin(2x)) within the interval ([0, 2\pi)). Please provide your answers as a comma-separated list.
2 Answers
4 sin 4x = -8 sin 2x
4*2sin 2x cos 2x = - 8sin 2x
or sin 2x ( cos 2x + 1) = 0
so sin 2x =0 or cos 2x = -1
or 2x = npi and 2x = npi
so x = n*pi/2 for n = 0, 1, 2,,3
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