Graph the function over a one-period interval.
-A generator produces an alternating current according to the equation $\mathrm { I } = 24 \sin 14 \pi \mathrm { t }$, where $\mathrm { t }$ is time in seconds and I is the current in amperes. What is the smallest time $t$ such that $\mathrm { I } = 12 ?$
A) $\frac { 1 } { 84 } \sec$

B) $\frac { 1 } { 28 } \mathrm { sec }$

C) $\frac { 1 } { 56 } \mathrm { sec }$

D) $\frac { 1 } { 42 } \mathrm { sec }$

Question

Graph the function over a one-period interval.
-A generator produces an alternating current according to the equation $\mathrm { I } = 24 \sin 14 \pi \mathrm { t }$, where $\mathrm { t }$ is time in seconds and I is the current in amperes. What is the smallest time $t$ such that $\mathrm { I } = 12 ?$
A) $\frac { 1 } { 84 } \sec$

B) $\frac { 1 } { 28 } \mathrm { sec }$

C) $\frac { 1 } { 56 } \mathrm { sec }$

D) $\frac { 1 } { 42 } \mathrm { sec }$

Quizplus · Accepted Answer

The period of the function is $\frac { 2 \pi } { 14 \pi } = \frac { 1 } { 7 } $ seconds. To find the smallest time $t$ such that $\mathrm { I } = 12$, we solve the equation $\mathrm { I } = 24 \sin 14 \pi \mathrm { t } = 12$. This gives $\sin 14 \pi \mathrm { t } = \frac { 1 } { 2 }$, which has solutions at $t = \frac { 1 } { 84 } + \frac { k } { 28 }$, where $k$ is an integer. The smallest positive value of $t$ is $t = \frac { 1 } { 84 }$.

Graph the Function Over a One-Period Interval I=24sin⁡14πt\mathrm { I } = 24 \sin 14 \pi \mathrm { t }I=24sin14πt

Graph the Function Over a One-Period Interval $\mathrm { I } = 24 \sin 14 \pi \mathrm { t }$