Questions: Graph the function. What is the period of the function? y=cos(1/8)x

Transcript text: Graph the function. What is the period of the function? \[ y=\cos \frac{1}{8} x \]

Solution

Solution Steps

Step 1: Identify the function to be graphed

The function to be graphed is: \[ y = \cos \frac{1}{8} x \]

Step 2: Determine the period of the function

The period $ T $ of the function $ y = \cos \left( \frac{1}{8} x \right) $ can be found using the formula for the period of a cosine function $ y = \cos(bx) $, which is $ T = \frac{2\pi}{b} $.

Here, $ b = \frac{1}{8} $, so: \[ T = \frac{2\pi}{\frac{1}{8}} = 16\pi \]

Final Answer

The period of the function $ y = \cos \frac{1}{8} x $ is $ 16\pi $.

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