The description you provided contains some inaccuracies. Here’s a correct analysis of the sine wave based on your information:
- The sine wave has a minimum value of -1 and a maximum value of 1, which is characteristic of the standard sine function.
- The wave completes one full cycle in the interval from 0 to \(2\pi\).
- The sine wave starts at (0, 0), rises to its maximum value of 1 at \( \frac{\pi}{2} \), returns to 0 at \( \pi \), reaches its minimum value of -1 at \( \frac{3\pi}{2} \), and returns to 0 again at \(2\pi\).
So, the correct description of the graph of a sine wave would be:
- The sine wave starts at (0, 0), increases to a maximum of 1 at \( \frac{\pi}{2} \), returns to 0 at \( \pi \), decreases to a minimum of -1 at \( \frac{3\pi}{2} \), and returns to 0 again at \( 2\pi \).
It seems there was confusion in your original description regarding the points where the wave reaches its maximum and minimum values.
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