A $84$ turn, $10\mathrm{.}0$ cm diameter coil rotates at an angular velocity of $8\mathrm{.}00$ rad$/$s in a $1\mathrm{.}22$ T field, starting with the normal of the plane of the coil perpendicular to the field. Assume that the positive max emf is reached first.

$($a$)$ What is the peak emf?

$($b$)$ At what time is the peak emf first reached?

$($c$)$ At what time is the emf first at its most negative?

$($d$)$ What is the period of the AC voltage output?