$*28.$ Find the average power loss and power factor for each of the circuits whose input current and voltage are as follows:

a$.v=60sin(t+30)$

$i=15sin(t+60)$

b$.v=-50sin(t-20)$

$i=-2sin(t-20)$

c$.v=50sin(t+80)$

$i=3cos(t-20)$

d$.v=75sin(t-5)$

$i=0\mathrm{.}08sin(t+35)$

$37.$ Convert the following from rectangular to polar form:

a$.4+j3$

b$.2+j2$

c$.4+j12$

d$.1000+j50$

e$.-1000+j4000$

f$.-0\mathrm{.}4+j0\mathrm{.}8$

$40.$ Convert the following from polar to rectangular form:

a$.\frac{42}{{?}_{0\mathrm{.}15}}$

b$.\frac{2002}{{?}_{-}}60$

c$.\frac{0\mathrm{.}006}{{?}_{-}}120$

$52.$ Express the following in phasor form:

a$.\sqrt[\phantom{2}]{2}(160)sin(t+30)$

b$.$

c$.100sin(t-90)$

$54.$ Express the following phasor currents and voltages as sine waves if the frequency is $60$ Hz :

a$.I=40\frac{A}{{?}_{20}}$

b$.V=120\frac{V}{{?}_{10}}$

$55.$ For the system in Fig. $14\mathrm{.}82,$ find the sinusoidal expression for the unknown voltage $v_a$ if

$e_{in}=60sin(377t+90)$

For the system in Fig. $14\mathrm{.}83,$ find the sinusoidal expression for the unknown current $i_1$ if

$i_s=20{10}^{-6}sin(t+60)$