1)Solve equation- sin 2 theta -1 = cos2 theta
2)alternating currents i1 and i2 flow into a circuit node. output current is

i= i1 + i2 if i1 =5 sin( 50t + pye/3) and i2 =6 cos 50t
calculate the amplitude of i and the first time it occurs .

3)Power, p,in an electric circuit is given by p= iv where v= voltage and i is
current. Calculate the maximum power if

v= 0.02 sin(100pye t) volts
i=0.06sin(100pye t +pye/4)amps
Calculate the first time the power reaches amaximum value