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Solve this equation fo rx in the interval 0<=x<=360
3sinxtanx=8

I would do it this way:
sinxtanx = 8/3
sinx(sinx/cosx)=8/3
sin^2x/cosx = 8/3
(1-cos^2x)/cosx=8/3
cross-multiply
3 - 3cos^2x = 8cosx
3cos^2x + 8cosx - 3 = 0
(3cosx-1)(cosx+3)=0
cosx=1/3 or cosx = -3
the last one is not possible
so x = arccos(1/3)=70.5º
or 289.5º (in the fourth quadrant)

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Edward

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