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a. Let f(x)=7sin(4x). What is the period of f ? Preview Enter a mathematical expression [more..]

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

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Q. a. Let f(x)=7sin⁡(4x) f(x)=7 \sin (4 x) . What is the period of f f ?\newlinePreview\newlineEnter a mathematical expression [more..]
  1. Understand sine function: To find the period of the function f(x)=7sin⁡(4x)f(x) = 7\sin(4x), we need to understand the general form of a sine function, which is f(x)=Asin⁡(Bx+C)+Df(x) = A\sin(Bx + C) + D, where:\newline- AA is the amplitude,\newline- BB affects the period of the function,\newline- CC is the phase shift, and\newline- DD is the vertical shift.\newlineThe period of the sine function is given by the formula Period = (2π)/∣B∣(2\pi) / |B|.
  2. Identify coefficient B: In the given function f(x)=7sin⁡(4x)f(x) = 7\sin(4x), the coefficient BB in front of xx is 44. Therefore, we can use the formula for the period of the sine function to find the period of ff.\newlinePeriod of ff = (2π)/∣4∣(2\pi) / |4|
  3. Calculate period: Now we calculate the period using the value of BB we found in the previous step.\newlinePeriod of f=2π4f = \frac{2\pi}{4}\newlinePeriod of f=π2f = \frac{\pi}{2}

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