Question 1081748
{{{ drawing(400,400, -1.5,1.5,-1.5,1.5,
          grid(1),
           line(0,0, 0.86603, 1/2),
           line(0.86603,0, 0.86603, 1/2),
locate(0.43,-0.05,x),
locate(0.90,0.25,y),
locate(0.43,0.4,r),
locate(0.1,0.1,theta),
           circle(0,0,1)
) }}}
—

Here {{{ theta = 30^o }}}   

We know {{{sin(30^o) = 1/2 }}}  and  {{{ sin(theta) = y/r }}}  so by drawing a right triangle within the unit circle, we know {{{ r=1 }}} and therefore {{{ y = 1/2 }}}  

Notice how the other angle must be {{{ 180^o - 30^o = 60^o }}} because all angles of the triangle must sum to {{{ 180^o }}}.   That means {{{ sin(60^o) = x/r = x/1 = x }}}

We can find x by the Pythagorean theorem:   {{{ r^2 = x^2 + y^2 }}}

   {{{ 1^2 = x^2 + (1/2)^2 }}}
{{{  x^2 = 1-(1/2)^2 = 1-1/4 = 3/4 }}}  —>  {{{ x = sqrt(3/4) = highlight(sqrt(3)/2) = sin(60^o) }}}