Solve the problem.
-Suppose that for an electrical appliance, voltage is given by $\mathrm { V } = 189 \sin 120 \pi \mathrm { t }$ and amperage by $I = 1.07 \sin 120 \pi t$, where $t$ is time in seconds. Use identities to write the wattage $W = V I$ in the form $\mathrm { W } = \mathrm { a } \cos \omega \mathrm { t } + \mathrm { c }$.
A) $W = - 101.115 \cos 120 \pi t + 101.115$
B) $W = - 101.115 \cos 240 \pi t + 101.115$
C) $\mathrm { W } = - 202.23 \cos 240 \pi \mathrm { t } + 202.23$
D) $\mathrm { W } = 101.115 \cos 240 \pi t - 101.115$

Question

Quizplus · Accepted Answer

The product of two sine functions with the same frequency can be expressed using the identity $\sin^2 x = \frac{1 - \cos 2x}{2}$. Thus, $W = VI = 189 \sin 120 \pi t \cdot 1.07 \sin 120 \pi t = 202.23 \sin^2 120 \pi t = 101.115 (1 - \cos 240 \pi t)$, which simplifies to $W = -101.115 \cos 240 \pi t + 101.115$.

Solve the Problem V=189sin⁡120πt\mathrm { V } = 189 \sin 120 \pi \mathrm { t }V=189sin120πt

Solve the Problem $\mathrm { V } = 189 \sin 120 \pi \mathrm { t }$