Why Is This Trig Equation So Challenging to Solve?

[BluePhone]

I have spent over an hour trying to solve this equation but I cannot seem to do anything with the equation after I get to the point where

.529cosx + 0.916sinx = 1

I've tried doing a million other substitutions and methods but I just don't know how I should go about finding x.

Any help appreciated, thanks.

 

[SammyS]

$A\sin x+B\cos x=\sqrt{A^2+B^2}\cdot\sin(x+\phi)\,,$ where $\displaystyle \phi = \arctan \left(\frac{B}{A}\right) + \begin{cases}0 & \text{if }A \ge 0, \\\pi & \text{if }A < 0,\end{cases}$

 

[BluePhone]

Thank you for the quick reply but I'm not sure what I need to do with that equation.

I tried substituting values and in the end I got x = -38.23 which is incorrect

Edit: For the love of... it worked! Tried it again and apparently I'd done some of mistake, but that formula is magical! I'd be interested in learning why it works but I've already spent about 2 hours on this question, so I will likely come back here to ask in the future.

Thanks so much!