Question

Math

Posted 4 months ago

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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
```

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Answer from Sia

Verified answer

Posted 4 months ago

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 $T = \frac{2\pi}{|b|}$.

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