Solve the problem.
-A generator produces an alternating current according to the equation $\mathrm { I } = 16 \sin 88 \pi \mathrm { t }$, where $t$ is time in seconds and $\mathrm { I }$ is the current in amperes. What is the smallest time $\mathrm { t }$ such that $\mathrm { I } = 8$ ?
A) $\frac { 1 } { 528 } \mathrm { sec }$
B) $\frac { 1 } { 352 } \mathrm { sec }$
C) $\frac { 1 } { 176 } \mathrm { sec }$
D) $\frac { 1 } { 264 } \mathrm { sec }$

Question

Quizplus · Accepted Answer

Given $I = 16 \sin 88\pi t$ and $I = 8$, we solve $8 = 16 \sin 88\pi t$ to find $t$. Simplifying, $\sin 88\pi t = \frac{1}{2}$. The smallest positive $t$ for which this is true, given the frequency of the sine function, is $\frac{1}{528}$ sec.

Solve the Problem I=16sin⁡88πt\mathrm { I } = 16 \sin 88 \pi \mathrm { t }I=16sin88πt

Solve the Problem $\mathrm { I } = 16 \sin 88 \pi \mathrm { t }$