I am solving these trigonometric equations:
$-10.0317 = 10.0458 \times \sin(7.1726 \times 10^{-4} \times t)$
$-0.5319 = 10.0458 \times \cos(7.1726 \times 10^{-4} \times t)$
I solved the sin equation like:
$t = \frac{arcsin(\frac{-10.0317}{10.0458})}{7.1726 \times 10^{-4}} = -2116.119185$
$t = \frac{\pi - arcsin(\frac{-10.0317}{10.0458})}{7.1726 \times 10^{-4}} = 6496.110616$
I solved the cos equation like:
$t = \frac{arccos(\frac{-0.5319}{10.0458})}{7.1726 \times 10^{-4}} = 2263.849368$
$t = \frac{- \arccos(\frac{-10.0317}{10.0458})}{7.1726 \times 10^{-4}} = - 2263.849368$
None of cos or sin have any solution in common, but then we have the period
$p = \frac{2 \times \pi}{7.1726 \times 10^{-4}} = 8759.982861$
So both $2263.849368$ and $6496.110616$ will be the solution but I can only have one solution for t so how do I know which one is correct. Also someone told me that the sin equation will be solved like:
$t = \frac{\pi - arcsin(\frac{-10.0317}{-10.0458})}{7.1726 \times 10^{-4}} = 2263.849368$
I have no I idea how they made the denominatior negative in the arcsin.