the voltage E in volts in a circuit after t seconds (t70) is given by E=12 sin(120pi times t). After how many seconds does the voltage first reach 6 volts?
To find the time at which the voltage first reaches 6 volts, we need to solve the equation E = 6.
Given that E = 12 sin(120πt), we can set up the equation as follows:
6 = 12 sin(120πt)
To solve for t, we need to isolate the variable t. Divide both sides of the equation by 12:
6/12 = sin(120πt)/12
Simplifying:
1/2 = sin(120πt)/12
To eliminate the fraction on the right side, we can multiply both sides by 12:
(12)(1/2) = sin(120πt)
6 = sin(120πt)
Now, we have:
sin(120πt) = 6
However, the sine function only takes values between -1 and 1. Since 6 is outside this range, there is no value of t that satisfies this equation. Therefore, the voltage never reaches 6 volts in this circuit.