Solve the problem.
-In an electrical circuit, let $\mathrm { V }$ represent the electromagnetic force in volts at $\mathrm { t }$ seconds. Assume $\mathrm { V } = \cos 2 \pi \mathrm { t }$. Find the smallest positive value of $\mathrm { t }$ where $0 \leq \mathrm { t } \leq \frac { 1 } { 2 }$ for $\mathrm { V } = \frac { \sqrt { 2 } } { 2 }$.

Question

Quizplus · Accepted Answer

To find the smallest positive value of $t$ where $V = \frac{\sqrt{2}}{2}$, we set $\cos 2\pi t = \frac{\sqrt{2}}{2}$. Recognizing that $\cos 45^\circ = \cos \frac{\pi}{4} = \frac{\sqrt{2}}{2}$, we solve $2\pi t = \frac{\pi}{4}$ for $t$, giving $t = \frac{1}{8}$ sec as the smallest positive solution within the given interval.

Solve the Problem V\mathrm { V }V Represent the Electromagnetic Force in Volts At

Solve the Problem $\mathrm { V }$ Represent the Electromagnetic Force in Volts At