Answer
$\frac{\sqrt {15}}{8}$
Work Step by Step
$sin^{2}t$ + $cos^{2}t$ = 1
sin t = $\frac{7}{8}$
$(\frac{7}{8})^{2}$ + $cos^{2}t$ = 1
$\frac{49}{64}$ + $cos^{2}t$ = 1
$cos^{2}t$ = 1 -$\frac{49}{64}$
$cos^{2}t$ = $\frac{15}{64}$
cos t = $\sqrt \frac{15}{64}$ = $\frac{\sqrt {15}}{8}$