The sine wave starts at $$0$$, reaches a maximum of `____` at $$ \frac{\pi}{2} $$, returns to $$0$$ at `____`, reaches a minimum of `____` at $$\frac{3\pi}{2}$$, and repeats.

Flashcard 8 - Quantitative Reasoning Flashcard Set for the CLT

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$1$; $\pi$; $-1$

Explanation:

The sine function is periodic, and its graph follows a smooth wave-like pattern.

Starting at $0$ at $x = 0$, it reaches its maximum value of $1$ at $\frac{\pi}{2}$, then returns to $0$ at $\pi$. The graph then dips to its minimum value of $-1$ at $\frac{3\pi}{2}$, before returning to $0$ again at $2\pi$.

This cycle repeats indefinitely, showing the sine wave’s periodic nature with a period of $2\pi$.

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