Solve the problem.
-The function
$$I ( t ) = 40 \sin \left( 60 \pi t - \frac { \pi } { 2 } \right)$$ represents the amperes of current produced by an electric generator as a function of time t, where t is measured in seconds. Find the smallest value of t for which the current is 20 amperes. Round your answer to three decimal
Places, if necessary.
A) 0.008
B) 0.011
C) 0.017
D) 0.033

Question

Quizplus · Accepted Answer

To find the smallest value of $t$ for which $I(t) = 20$ amperes, we set the equation $40 \sin(60\pi t - \frac{\pi}{2}) = 20$ and solve for $t$. Dividing both sides by 40 gives $\sin(60\pi t - \frac{\pi}{2}) = 0.5$. Using the inverse sine function, we find that $60\pi t - \frac{\pi}{2} = \frac{\pi}{6}$ or $60\pi t - \frac{\pi}{2} = \frac{5\pi}{6}$ due to the periodic nature of the sine function. Solving the first equation for $t$ gives $t = \frac{1}{60} + \frac{1}{120} = 0.011$, which is the smallest positive value of $t$ that satisfies the equation.

Solve the Problem I(t)=40sin⁡(60πt−π2)I ( t ) = 40 \sin \left( 60 \pi t - \frac { \pi } { 2 } \right)I(t)=40sin(60πt−2π​)

Solve the Problem $I ( t ) = 40 \sin \left( 60 \pi t - \frac { \pi } { 2 } \right)$