Solve the equation for solutions over the interval [0, $[ 0,2 \pi )$ ). Write solutions as exact values or to four decimal places, as
appropriate.
-The output voltage for an AC generator is approximated by $\mathrm { v } = 156 \cos \left( 120 \pi \mathrm { t } - \frac { \pi } { 3 } \right)$. Find the smallest positive value of $\mathrm { t }$ for which the output is 144 volts. Round values to 4 decimal places.

Question

Quizplus · Accepted Answer

To find the smallest positive value of $t$ for which the output voltage $v$ is 144 volts, we set the equation $156 \cos(120\pi t - \frac{\pi}{3}) = 144$ and solve for $t$. Dividing both sides by 156 gives $\cos(120\pi t - \frac{\pi}{3}) = \frac{144}{156} = \frac{12}{13}$. Using the inverse cosine function and solving for $t$ yields $t = \frac{1}{120\pi}(\cos^{-1}(\frac{12}{13}) + \frac{\pi}{3})$, which, when calculated, gives the smallest positive value of $t$ as approximately 0.0038.

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 $[ 0,2 \pi )$