Subjects trigonometry

Function Period

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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 $\frac{2\pi}{|b|}$.