Write the Expression in Terms of Sine and Cosine, and Simplify

Multiple Choice

Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.
-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 $I$ 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) $P = R A ^ { 2 } \sin ^ { 2 } ( 2 \pi f t ) ; P = - R A ^ { 2 } \cos ^ { 2 } ( 2 \pi f t )$
B) $P = R A \sin ^ { 2 } ( 2 \pi f t ) ; P = R A - \cos ^ { 2 } ( 2 \pi f t )$
C) $P = R A ^ { 2 } \sin ^ { 2 } ( 2 \pi f \mathrm { ft } ) ; P = R A ^ { 2 } - R A ^ { 2 } \cos ^ { 2 } ( 2 \pi f t )$
D) $P = R A \sin ^ { 2 } ( 2 \pi f \mathrm { ft } ) ; P = R A - R A \cos ^ { 2 } ( 2 \pi f t )$