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$\begin{array}{l}{\text { Find the phasor transform of each trigonometric function: }} \\ {\begin{array}{l}{\text { a) } v=170 \cos \left(377 t-40^{\circ}\right) \mathrm{V}} \\ {\text { b) } i=10 \sin \left(1000 t+20^{\circ}\right) \mathrm{A}} \\ {\text { c) } i=\left[5 \cos \left(\omega t+36.87^{\circ}\right)+10 \cos \left(\omega t-53.113^{\circ}\right)\right] \mathrm{A}}\end{array}}\end{array}$

(1) $V=V_{m} cos (\omega t+\phi)$                            (V)

$V=70 \cos (\omega t+40)$

$V^{'}=V_{m} \angle \phi=70 \angle 40$                                (V)

(2) $i=10 \sin (1000 t+20^{\circ})$                                (A)

$i=10 \cos [1000 t+20-90]$

$i=10 \cos [1000t-70]$

$i=I_m \angle \phi=10 \angle -70$                                    (A)

(3) $i=5 cos (\omega t+36.87^{\circ})+10 cos [\omega t-53.13]$

$i=5 \angle 36.87+10 \angle -53.13$

$i=11.18 \angle -26.565^{\circ}$                            (A)

$\begin{array}{l}{\text { Find the time-domain expression corresponding to each phasor }} \\ {\qquad \begin{array}{l}{\text { a) } \mathbf{V}=18.6 \angle-54^{\circ} \mathrm{V} .} \\ {\text { b) } \mathbf{I}=\left(20 \angle 45^{\circ}-50 \angle\left(-30^{\circ}\right) \mathrm{mA}\right.}\end{array}}\end{array}$

(1) $V=18.6 \ \angle -54$

$V=V_{n}cos(\omega t+\phi)$

$V=18.6 \cos (\omega t-54)$

(2) $I=20 \angle 4{5}-50 \angle {-30}=48.81 \ \angle26.68$

$I=I_m cos (\omega t+\phi)=48.81 cos [\omega t+126.68]$