Question 149437
{{{3*sin^2(x)-8*sin(x)-3=0}}}
Let's substitute {{{u=sin(x)}}}
{{{3u^2-8u-3=0}}} Quadratic equation in u.
{{{(3u+1)(u-3)=0}}}Factor the quadratic equation. 
First factor:
{{{3u+1=0}}}
{{{3sin(x)+1=0}}}
{{{3sin(x)=-1}}}
{{{sin(x)=-1/3}}}
2 solutions for this equation.
x=340.53 degrees and x=199.47 degrees
Second factor:
{{{u-3=0}}}
{{{sin(x)-3=0}}}
{{{sin(x)=3}}}
sin(x) is never greater than 1, so there are no additional solutions.
Below is the graph of the function.
{{{ graph( 300, 200, 0, 7, -10,10, 3*(sin(x)^2)-8*sin(x)-3) }}} 
Note : x axis is measured in radians.
360 degrees = 6.28 radians
340.53 degrees =  5.94 radians
199.47 degrees =  3.48 radians