Question 1102807
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We are to find all the solutions for x of the equation 2 sin(3x) - 1 = 0 in the interval [0, 2pi).  The first thing we should note is that if x is in the interval [0, 2pi) then 3x is in the interval [0, 6pi).<br>
{{{2 sin(3x) - 1 = 0}}}
{{{2 sin(3x) = 1}}}
{{{sin(3x) = 1/2}}}<br>
The solutions for 3x on the interval [0, 6pi) are
pi/6, 5pi/6, 13pi/6, 17pi/6, 25pi/6, and 29pi/6<br>
The solutions for x on the interval [0,2pi) are
pi/18, 5pi/18, 13pi/18, 17pi/18, 25pi/18, and 29pi/18