Function Period
1. Let's clarify the problem: You asked, "so what is the period?" This usually refers to the period of a periodic function, such as sine, cosine, or any repeating wave.
2. The period of a function is the length of the smallest interval over which the function repeats itself. For example, the sine function $y=\sin(x)$ has a period of $2\pi$ because $\sin(x+2\pi) = \sin(x)$ for all $x$.
3. The general formula for the period $T$ of a function $y=\sin(bx)$ or $y=\cos(bx)$ is:
$$
T = \frac{2\pi}{|b|}
$$
where $b$ is the coefficient of $x$ inside the function.
4. Important rules:
- The period is always positive.
- If the function is not periodic, it does not have a period.
5. If you provide a specific function, I can calculate its period step-by-step.
6. Without a specific function, the concept above explains how to find the period.
Final answer: The period depends on the function. For $y=\sin(bx)$ or $y=\cos(bx)$, the period is $\frac{2\pi}{|b|}$.