Verify That the Equation Is an Identity $\mathrm { V } _ { 1 } = 120 \sin ( 220 \pi \mathrm { t } )$

Multiple Choice

Verify that the equation is an identity.
-Two voltages, $\mathrm { V } _ { 1 } = 120 \sin ( 220 \pi \mathrm { t } )$ and $\mathrm { V } _ { 2 } = 90 \cos ( 220 \pi \mathrm { t } )$ , are added in a circuit to produce the sum $\mathrm { V } = \mathrm { V } _ { 1 } + \mathrm { V } _ { 2 }$ . Graph $\mathrm { V }$ in $[ - 0.02,0.02,0.002 ]$ by $[ - 250,250,20 ]$ and use the graph to estimate values for a and $\mathrm { k }$ so that $\mathrm { V } = \mathrm { a } \sin ( 220 \pi \mathrm { t } + \mathrm { k } )$ . Round $\mathrm { k }$ to the nearest ten-thousandth, if necessary.

A) $a = 150 ; k = 640.8999$
B) $\mathrm { a } = 15 ; \mathrm { k } = 0.6435$
C) $\mathrm { a } = 150 ; \mathrm { k } = 444.7557$
D) $\mathrm { a } = 150 ; \mathrm { k } = 0.6435$