Answer
$t = \frac{50}{\pi}~arccos(\frac{d-550}{450})$
Work Step by Step
$d = 550+450~cos(\frac{\pi}{50}~t)$
$450~cos(\frac{\pi}{50}~t) = d-550$
$cos(\frac{\pi}{50}~t) = \frac{d-550}{450}$
$\frac{\pi}{50}~t = arccos(\frac{d-550}{450})$
$t = \frac{50}{\pi}~arccos(\frac{d-550}{450})$
