Solve the Problem $\mathrm { P } = \mathrm { RI } ^ { 2 }$

Solve the problem.
-The power dissipated in an electric circuit is given by the expression $\mathrm { P } = \mathrm { RI } ^ { 2 }$ , where $\mathrm { R }$ is the resistance of the circuit and $\mathrm { I }$ is the current through the circuit. For a sinusoidal alternating current, the current might be represented by the relation $\mathrm { I } = \mathrm { A } \sin ( 2 \pi \mathrm { ft } )$ , where $\mathrm { A }$ is the amplitude, $\mathrm { f }$ is the frequency, and $t$ is time. Write an expression for P involving the sine function, and use a fundamental identity to write $P$ in terms of the cosine function.

A) $P = R A \sin ^ { 2 } ( 2 \pi f \mathrm { t } ) ; \mathrm { P } = \mathrm { RA } - \mathrm { RA } \cos ^ { 2 } ( 2 \pi \mathrm { ft } )$
B) $P = R A ^ { 2 } \sin ^ { 2 } ( 2 \pi f t ) ; P = - R A ^ { 2 } \cos ^ { 2 } ( 2 \pi f t )$
C) $P = R A \sin ^ { 2 } ( 2 \pi f \mathrm { ft } ) ; \mathrm { P } = \mathrm { RA } - \cos ^ { 2 } ( 2 \pi \mathrm { ft } )$
D) $P = R A ^ { 2 } \sin ^ { 2 } ( 2 \pi f t ) ; P = R A ^ { 2 } - R A ^ { 2 } \cos ^ { 2 } ( 2 \pi f t )$