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a. Let f(x)=7sin⁡(4x)f(x)=7\sin(4x). What is the period of ff?\newlinePreview\newlineEnter a mathematical expression [more...]

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Write variable expressions for arithmetic sequencesright chevron icon

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Q. a. Let f(x)=7sin⁡(4x)f(x)=7\sin(4x). What is the period of ff?\newlinePreview\newlineEnter a mathematical expression [more...]
  1. Sine Function Period: The period of a sine function is determined by the coefficient of xx inside the sine function. The general form of a sine function is sin⁡(bx)\sin(bx), where the period is given by 2πb\frac{2\pi}{b}. In the given function f(x)=7sin⁡(4x)f(x) = 7\sin(4x), the coefficient of xx is 44.
  2. General Form: To find the period of f(x)f(x), we use the formula for the period of a sine function, which is 2π2\pi divided by the coefficient of xx. So, the period of f(x)=7sin⁡(4x)f(x) = 7\sin(4x) is 2π4\frac{2\pi}{4}.
  3. Calculate Period: Now we calculate the period: 2π4=π2\frac{2\pi}{4} = \frac{\pi}{2}. This means that the function f(x)=7sin⁡(4x)f(x) = 7\sin(4x) completes one full cycle every π2\frac{\pi}{2} units.

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