An electric resistance space heater rated at 456 Watts for a voltage source of v(t) = 169.7 sin(2  60t) V has a thermostatically controlled switch. The heater periodically switches on for 5 seconds and off for 7 seconds. Determine
a) ) the instantaneous power,
b) the average power over the l2-seconds cycle, and
c) the electric energy converted to heat in each cycle.