What is the period of y=-5cos((pi)/(8)x)+3? Give an exact value. units

Identify Standard Form: Identify the standard form of a cosine function and its period. The standard form of a cosine function is y = A*cos(Bx - C) + D, where: - A is the amplitude, - B affects the period of the function, - C is the phase shift, and - D is the vertical shift. The period of the standard cosine function cos(x) is 2π. For the function y = A*cos(Bx - C) + D, the period is given by the formula Period = 2π / |B|.Determine Value of B: Determine the value of B in the given function. In the given function y = -5cos((pi)/(8)x) + 3, the value of B is (pi)/(8).Calculate Period: Calculate the period of the given function using the formula. Using the formula Period = 2π / |B|, we substitute B with (pi)/(8): Period = 2π / |(pi)/(8)| = 2π / (pi/8) = 2π * (8/pi) = 16.

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What is the period of

y=-5cos((pi)/(8)x)+3?
Give an exact value.
units

What is the period of $\newline$ $y=-5 \cos \left(\frac{\pi}{8} x\right)+3 ?$ $\newline$ Give an exact value. $\newline$ units

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Q. What is the period of

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y=-5 \cos \left(\frac{\pi}{8} x\right)+3 ?

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Give an exact value.

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units

Identify Standard Form: Identify the standard form of a cosine function and its period. $\newline$ The standard form of a cosine function is $y = A\cos(Bx - C) + D$ , where: $\newline$ - $A$ is the amplitude, $\newline$ - $B$ affects the period of the function, $\newline$ - $C$ is the phase shift, and $\newline$ - $D$ is the vertical shift. $\newline$ The period of the standard cosine function $\cos(x)$ is $2\pi$ . For the function $y = A\cos(Bx - C) + D$ , the period is given by the formula $\text{Period} = \frac{2\pi}{|B|}$ .
Determine Value of B: Determine the value of B in the given function. $\newline$ In the given function $y = -5\cos\left(\frac{\pi}{8}x\right) + 3$ , the value of B is $\frac{\pi}{8}$ .
Calculate Period: Calculate the period of the given function using the formula. $\newline$ Using the formula $\text{Period} = \frac{2\pi}{|B|}$ , we substitute $B$ with $\frac{\pi}{8}$ : $\newline$ $\text{Period} = \frac{2\pi}{|\frac{\pi}{8}|} = \frac{2\pi}{\frac{\pi}{8}} = 2\pi \times \frac{8}{\pi} = 16$ .