Lissajous Figures Are Used in the Study of Electrical Circuits $\varphi$

Multiple Choice

Lissajous figures are used in the study of electrical circuits to determine the phase difference $\varphi$ between a known voltage $V _ { 1 } ( t ) = A \sin ( a t )$ and an unknown voltage $V _ { 2 } ( t ) = B \sin ( ω t + \varphi )$
$a \mathrm{dt}$ having the same frequency. The voltages are graphed parametrically as $x = V _ { 1 } ( t )$ and $y = V _ { 2 } ( t )$ . If $\varphi$ is acute, then $\varphi = \sin ^ { - 1 } \frac { y _ { \mathrm { int } } } { y _ { \max } }$ where y _int is the nonnegative y -intercept and y _max is the maximum y -value on the curve. Graph the parametric curve and use the graph to approximate $\varphi$ in degrees if $\begin{array} { c } V _ { 1 } ( t ) = 40 \sin ( 60 \pi t ) , V _ { 2 } ( t ) = 90 \cos ( 60 \pi t - \pi / 3 ) , \\0 \leq t \leq 0.035\end{array}$

A) $30 ^ { \circ }$
B) $90 ^ { \circ }$
C) $60 ^ { \circ }$
D) $45 ^ { \circ }$
E) $15 ^ { \circ }$