Solve the Problem $$e = 20 \sin \left( \frac { \pi t } { 4 } - \frac { \pi } { 2 } \right)$$

Multiple Choice

Solve the problem.
-A coil of wire rotating in a magnetic field induces a voltage given by
$$e = 20 \sin \left( \frac { \pi t } { 4 } - \frac { \pi } { 2 } \right)$$
where $t$ is time in seconds. Find the smallest positive time to produce a voltage of $10 \sqrt { 2 }$ .

A) $3 \mathrm { sec }$
B) $3 \pi \mathrm { sec }$
C) $2.8 \pi \mathrm { sec }$
D) $2.8 \mathrm { sec }$