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Chapter 4: Problem 14

State the period of each function. $$y=-3 \cot \frac{2 x}{3}$$

Short Answer

Expert verified
The period of the function \( y = -3 \cot(\frac{2x}{3}) \) is \( \frac{3\pi}{2} \).

Step by step solution

01

Determine the period of the base function

The base function here is the cotangent function, which has a period of \( \pi \) in radians. So, \( P = \pi \).
02

Determine the coefficient of x

The coefficient of \( x \) in the function \( y = -3 \cot(\frac{2x}{3}) \) is \( \frac{2}{3} \). So \( B = \frac{2}{3} \).
03

Calculate the period of the transformed function

To find the period of the transformed function, we use the formula \(\frac{P}{|B|}\). Substituting \( P = \pi \) and \( B = \frac{2}{3} \), we get \(\frac{\pi}{|\frac{2}{3}|} = \frac{3\pi}{2}.\)

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