This problem is part of the analysis of a statics problem.

There is a force P applied to a system which is 0.589kN. I need to determine if there is such an angle that would allow us to apply 86.6% of P and still be able to cut through a board that requires 3.5kN of force to cut.

All simplified I end up with this:

3.5 = 3.03cos x + 2.04sin x

How do I solve for x? I think you take the derivative of the expression and then solve.

2.04 / 3.03 = sinx / cosx

Is this the correct approach?

Also are there two angles that would satisfy this equation?