## Trigonometry (11th Edition) Clone

To produce voltage $E=0$, it takes at least 2 seconds.
$$E=20\sin(\frac{\pi t}{4}-\frac{\pi}{2})$$ Since $t$ is time in seconds, the range of $t$ is $[0,\pi)$ For $E=0$, we get the equation $$20\sin(\frac{\pi t}{4}-\frac{\pi}{2})=0$$ $$\sin(\frac{\pi t}{4}-\frac{\pi}{2})=0$$ For $\frac{\pi t}{4}-\frac{\pi}{2}=0$, we would get $\sin(\frac{\pi t}{4}-\frac{\pi}{2})=0$. Also we would get the least positive $t$ through this. $$\frac{\pi t}{4}-\frac{\pi}{2}=0$$ $$\frac{\pi t}{4}=\frac{\pi}{2}$$ $$t=\frac{\pi}{2}\times\frac{4}{\pi}$$ $$t=2(seconds)$$ So to produce voltage $E=0$, it takes at least 2 seconds.
The passage contains a trigonometric problem and provides a detailed solution to find the time \( t \) when the voltage \( E \) is zero.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
## Trigonometry (11th Edition) Clone

To produce voltage $E=0$, it takes at least 2 seconds.
$$E=20\sin(\frac{\pi t}{4}-\frac{\pi}{2})$$ Since $t$ is time in seconds, the range of $t$ is $[0,\pi)$ For $E=0$, we get the equation $$20\sin(\frac{\pi t}{4}-\frac{\pi}{2})=0$$ $$\sin(\frac{\pi t}{4}-\frac{\pi}{2})=0$$ For $\frac{\pi t}{4}-\frac{\pi}{2}=0$, we would get $\sin(\frac{\pi t}{4}-\frac{\pi}{2})=0$. Also we would get the least positive $t$ through this. $$\frac{\pi t}{4}-\frac{\pi}{2}=0$$ $$\frac{\pi t}{4}=\frac{\pi}{2}$$ $$t=\frac{\pi}{2}\times\frac{4}{\pi}$$ $$t=2(seconds)$$ So to produce voltage $E=0$, it takes at least 2 seconds.
user
The passage contains a trigonometric problem and provides a detailed solution to find the time \( t \) when the voltage \( E \) is zero.

TYPE: SINGLE_QUESTION_WITH_ANSWER