To solve the equation
invert both sides, obtaining
This is not the only the solution. There are an infinite number of solutions. Typically though, we want solutions in the range 0° – 360°.
We can use the sine curve below to find the solutions.
Draw the horizontal line y=0.2 (because the equation to solve is sin x =0.2). Where this line crosses the curve, drop a line to the x - axis. The solution is where the line crosses the x – axis.
The sin curve has symmetry, so that
This often aids the search for a solution.
The two solutions are x=11.54° and x=168.46° .