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 cosine curve below to find the solutions.
Draw the horizontal line y=0.4 (because the equation to solve is cos x =0.4). Where this line crosses the curve, drop a line to the x - axis. The solution is where the line crosses the x – axis.
The cosine curve has symmetry, so that
This often aids the search for a solution.
The two solutions are x=66.42° and x=293.58° .