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What is the period of the function 
f(x)=3sin(2x-1)+4 ?
Give an exact value.
units

What is the period of the function f(x)=3sin(2x1)+4 f(x)=3 \sin (2 x-1)+4 ?\newlineGive an exact value.\newlineunits

Full solution

Q. What is the period of the function f(x)=3sin(2x1)+4 f(x)=3 \sin (2 x-1)+4 ?\newlineGive an exact value.\newlineunits
  1. Determining the Period: The period of a sine function is determined by the coefficient of x inside the sine function. The general form of a sine function is \sin(bx), where the period is given by \frac{22\pi}{b}.
  2. Finding the Coefficient of x: For the function f(x) = 33\sin(22x - 11) + 44, the coefficient of x inside the sine function is 22. Therefore, we can find the period by using the formula 22\pi/b, where b = 22.
  3. Using the Period Formula: Calculate the period using the formula: Period = 2π/b=2π/22\pi/b = 2\pi/2.
  4. Calculating the Period: Simplify the expression to find the period: Period = π\pi.

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