Question 281690
There's nothing wrong with using a graphical approach. You just need to keep in mind that the solutions will be approximate, which means that you need to figure out a way to get them into exact form. Since you are familiar with 0.5236 and 2.618 as {{{pi/6}}} and {{{5pi/6}}}, the second concern isn't really an issue. However, the approximate solutions may not be so easy to recognize in general. Because of this potential problem, I suggest to use an algebraic approach.



{{{r=2sin(theta)}}} Start with the second equation



{{{1=2sin(theta)}}} Plug in {{{r=1}}}



{{{1/2=sin(theta)}}} Divide both sides by 2.



{{{sin(theta)=1/2}}} Rearrange the equation.



{{{theta=pi/6}}} or {{{theta=5pi/6}}} Take the arcsine of both sides



Note: Since {{{sin(pi/6)=sin(5pi/6)=1/2}}}, this means that the arcsine of {{{1/2}}} is either {{{pi/6}}} or {{{5pi/6}}}. 



So the exact solutions for theta are {{{theta=pi/6}}} or {{{theta=5pi/6}}}



So you are correct.