Question 582240
{{{(sin(x))^2=1/2}}}
There is a positive and a negative value for {{{sin(x)}}}.
The positive solution is: {{{sin(x)=sqrt(1/2)=sqrt(2/4)=sqrt(2)/sqrt(4)=sqrt(2)/2=sin(pi/4)=sin(3pi/4)}}}
The negative solution is: {{{sin(x)=-sqrt(1/2)=-sqrt(2)/2=sin(5pi/4)=sin(7pi/4)}}}
Those four angles {{{pi/4}}}, {{{3pi/4}}}, {{{5pi/4}}} and {{{7pi/4}}} are the solution.
The reference angle is {{{pi/4}}}, or {{{45^o}}} for those allergic to {{{pi}}}.
For each (first quadrant) reference angle there is, in each of the other quadrants, a "reflection" angle that has the same absolute value for all trigonometric functions. It is {{{pi-angle}}}, the reflection on the y axis, for the second quadrant. It is {{{pi+angle}}}, the reflection on the origin, for the third quadrant, and {{{-angle}}}, or {{{2pi-angle}}} if you want it positive, the reflection on the x axis, for the third quadrant.