Use a Sum or Difference Identity to Find the Exact $\mathrm { V } _ { 1 } = 80 \sin ( 110 \pi \mathrm { t } )$

Multiple Choice

Use a sum or difference identity to find the exact value.
-Two voltages, $\mathrm { V } _ { 1 } = 80 \sin ( 110 \pi \mathrm { t } )$ and $\mathrm { V } _ { 2 } = 150 \cos ( 110 \pi \mathrm { t } )$ , are added in a circuit to produce the sum $V = V _ { 1 } + V _ { 2 }$ . Graph $V$ in $[ - 0.02,0.02,0.002 ]$ by $[ - 250,250,20 ]$ and use the graph to estimate values for $\mathrm { a }$ and $\mathrm { k }$ so that $\mathrm { V } = \mathrm { a } \sin ( 110 \pi \mathrm { t } + \mathrm { k } )$ . Round $\mathrm { k }$ to the nearest ten-thousandth, if necessary.

A) $a = 17 ; k = 1.0808$
B) $a = 170 ; k = 169.317$
C) $a = 170 ; \mathrm { k } = 1.0808$
D) $a = 170 ; k = 373.5108$