This equation is equivalent to
now squaring both sides
and now knowing that
Those equations to be completely solved require the solution of a cubic polynomial. We left this as an exercise.
A different method to the one below.
So the equation becomes
This equation is true iff
Finding general solutions will be left as an exercise
From the tables we know that :
I could solve this equation with
but it is beyond my capabilities.
If we play a little with the trigonometric circle we can find
We just need to divide the third degree equation by (y-0.5) and obtain the remainder solutions:
Remember the first solution:
x = pi/8 + (kpi)/4
x = - pi/4 + kpi
x = - (3pi/4) + kpi
Note that sin x = cos (pi/2 - x)
We have to solve these equations:
Finally, the general solutions are: