1. The problem is to understand and work with a trigonometric function. 2. Trigonometric functions relate angles to ratios of sides in right triangles and are periodic functions. 3. Common trigonometric functions include sine ($\sin$), cosine ($\cos$), and tangent ($\tan$). 4. For example, consider the function $y = \sin x$. 5. The sine function has a period of $2\pi$, meaning it repeats every $2\pi$ units. 6. It oscillates between $-1$ and $1$, with zeros at multiples of $\pi$. 7. The formula for sine is based on the unit circle: $\sin x$ is the y-coordinate of the point on the unit circle at angle $x$. 8. To analyze $y = \sin x$, we find intercepts where $\sin x = 0$, which are at $x = k\pi$ for integers $k$. 9. The extrema (maximum and minimum) occur at $x = \frac{\pi}{2} + k\pi$, with maximum $1$ and minimum $-1$. 10. Understanding these properties helps graph and solve equations involving sine.