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

Question

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the coefficient of $x$ inside the cosine function to determine the period. ‖ ‖ step 2 ⋮ The coefficient of $x$ is $-\frac{\pi}{2}$. The period of a cosine function is given by $T = \frac{2\pi}{|b|}$, where $b$ is the coefficient of $x$. ‖ ‖ step 3 ⋮ Substitute $-\frac{\pi}{2}$ for $b$ in the period formula: $T = \frac{2\pi}{|-\frac{\pi}{2}|}$. ‖ ‖ step 4 ⋮ Calculate the absolute value and simplify: $T = \frac{2\pi}{\frac{\pi}{2}} = 4$. ‖ ∻[question 1] Answer∻ ⚹ The period of the function $g(x) = -9\cos\left(-\frac{\pi}{2} x - 6\right) + 8$ is $4$ units. ⚹ ∻Key Concept∻ ⚹Period of a Cosine Function⚹ ∻Explanation∻ ⚹The period of a cosine function $cos(bx)$ is determined by the coefficient $b$ in front of $x$, using the formula $T = \frac{2\pi}{|b|}$.◊What is the formula for calculating the period of a trigonometric function?⍭ Generate me a similar question◊⚹

Sia