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

question 151

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) \(\mathrm { a } = 150 ; \mathrm { k } = 0.6435\)

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