After looking at the list of trigonometric identities, I can't seem to find a way to solve this. Is it solvable?
$\cos(\theta) + \sin(\theta) = x.$
What if I added another equation to the problem:
$-\sin(\theta) + \cos(\theta) = y,$ where $\theta$ is the same and $y$ is also known?
Thanks.
EDIT:
OK, so using the linear combinations I was able to whip out:
$a \sin(\theta) + b \cos(\theta) = x = \sqrt{a^2 + b^2} \sin(\theta + \phi),$ where $\phi = \arcsin \left( \frac{b}{\sqrt{a^2 + b^2}} \right) = \frac{\pi}{4}$ (as long as $a\geq 0$)
Giving me:
$x = \sin(\theta + \frac{\pi}{4}) \text{ and } \arcsin(x) - \frac{\pi}{4} = \theta.$
All set! Thanks!