The current, i, in amperes (A), passing though a wire is given by the equation:

i(t) = 8 sin(0.7t + 25), where t is the time, in seconds.

What is the approximate period of this function?

Question 16 options:

0.7 s

360 s

252 s

514 s

To find the period of the function \( i(t) = 8 \sin(0.7t + 25) \), we need to analyze the sine function within the equation.

The general form of a sine function is:

\[
i(t) = A \sin(Bt + C) + D
\]

Where:
- \( A \) is the amplitude,
- \( B \) affects the period of the function,
- \( C \) is the phase shift,
- \( D \) is the vertical shift.

The period \( T \) of a sine function is given by the formula:

\[
T = \frac{2\pi}{B}
\]

In the given equation, \( B = 0.7 \). Therefore, the period is:

\[
T = \frac{2\pi}{0.7}
\]

Now, let's calculate the period.

\[
T = \frac{2\pi}{0.7} \approx \frac{6.2832}{0.7} \approx 8.975 \, \text{seconds}
\]

So, the period of the function is approximately 8.975 seconds, which is much smaller than any of the given options. Since none of the provided options (0.7 s, 360 s, 252 s, 514 s) are close to this value, there might be an error in the options provided.

However, based on the standard calculation method, the period should be around **9 seconds**. Therefore, none of the provided options are correct based on this calculation.

Would you like to dive into more details, or have any further questions?

Here are 8 related questions to consider:
1. How is the amplitude of a sine wave determined?
2. What role does the phase shift \( C \) play in the sine function?
3. How does the value of \( B \) affect the frequency of the sine wave?
4. Can you derive the period for a cosine function in a similar scenario?
5. What is the physical significance of the amplitude in electrical signals?
6. How would a vertical shift \( D \) affect the sine function graph?
7. What is the general relationship between frequency and period?
8. How can you identify the phase shift from the sine function equation?

**Tip:** When dealing with trigonometric functions in electrical engineering, always remember that the period of the function is inversely proportional to the coefficient of the time variable inside the function.

Learn how to calculate the period of a sine function using the formula T = 2π / B. This example problem involves analyzing the function i(t) = 8 sin(0.7t + 25) and determining its periodicity. Discover the mathematical concepts of trigonometry and periodic functions. Suitable for advanced mathematics students.

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