What is the period of the function g(x)=-9cos(-(pi)/(2)x-6)+8? Give an exact value. units

Identify b value: The period of a cosine function of the form cos(bx) is 2π/|b|. In the given function g(x) = -9cos(-(π/2)x - 6) + 8, we need to identify the value of b to determine the period.Rewrite function: The function g(x) can be rewritten without the negative inside the cosine as g(x) = -9cos((π/2)x + 6) + 8, because cos(-θ) = cos(θ). This does not change the period of the function.Calculate period: Now, we can see that the coefficient b in front of x inside the cosine function is π/2. Therefore, the period of g(x) is 2π divided by |π/2|.Period calculation: Calculating the period, we have Period = 2π / |π/2| = 2π / (π/2) = (2π) * (2/π) = 4.Final period: The period of the function g(x) = -9cos((π/2)x + 6) + 8 is 4 units.

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What is the period of the function

g(x)=-9cos(-(pi)/(2)x-6)+8?
Give an exact value.
units

What is the period of the function $\newline$ $g(x)=-9 \cos \left(-\frac{\pi}{2} x-6\right)+8 ?$ $\newline$ Give an exact value. $\newline$ units

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Q. What is the period of the function

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g(x)=-9 \cos \left(-\frac{\pi}{2} x-6\right)+8 ?

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Give an exact value.

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units

Identify b value: The period of a cosine function of the form $\cos(bx)$ is $\frac{2\pi}{|b|}$ . In the given function $g(x) = -9\cos\left(-\left(\frac{\pi}{2}\right)x - 6\right) + 8$ , we need to identify the value of $b$ to determine the period.
Rewrite function: The function $g(x)$ can be rewritten without the negative inside the cosine as $g(x) = -9\cos\left(\frac{\pi}{2}x + 6\right) + 8$ , because $\cos(-\theta) = \cos(\theta)$ . This does not change the period of the function.
Calculate period: Now, we can see that the coefficient $b$ in front of $x$ inside the cosine function is $\pi/2$ . Therefore, the period of $g(x)$ is $2\pi$ divided by $|\pi/2|$ .
Period calculation: Calculating the period, we have Period = $\frac{2\pi}{|\pi/2|} = \frac{2\pi}{(\pi/2)} = (2\pi) \cdot (\frac{2}{\pi}) = 4$ .
Final period: The period of the function $g(x) = -9\cos\left(\frac{\pi}{2}x + 6\right) + 8$ is $4$ units.