Solve the equation for solutions over the interval [0, $[ 0,2 \pi )$ ). Write solutions as exact values or to four decimal places, as
appropriate.
-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 $0 \leq t \leq \frac{1}{2}$ for $V = \frac{\sqrt{2}}{2}$, we set $\cos 2\pi t = \frac{\sqrt{2}}{2}$. The equation $\cos \theta = \frac{\sqrt{2}}{2}$ has solutions at $\theta = \frac{\pi}{4}$ and $\theta = \frac{7\pi}{4}$ within one cycle of the cosine function. Since $2\pi t = \frac{\pi}{4}$, solving for $t$ gives $t = \frac{1}{8}$ seconds. This is the smallest positive value of $t$ in the given interval that satisfies the equation.

Solve the Equation for Solutions Over the Interval [0 [0,2π)[ 0,2 \pi )[0,2π)

Solve the Equation for Solutions Over the Interval [0 $[ 0,2 \pi )$