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Chapter 4: Problem 18

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

Short Answer

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

Step by step solution

01

Recognize the Function

Recognize that the function \(y = \cot (\frac{\pi x}{3})\) is a cotangent function where \(\cot\) is the cotangent function and \(\frac{\pi x}{3}\) is the input into the function.
02

Identify the Coefficient of x

The coefficient of x, denoted as 'b' in this case, is the value \(\frac{\pi}{3}\). This coefficient is integral in determining the period of the cotangent function.
03

Apply the Formula for Cotangent

The period of a cotangent function is given by the formula \(\pi/b\). Substituting the value for 'b' from Step 2 into the formula, the period becomes \(\pi / (\frac{\pi}{3})\). By dividing \(\pi\) by \(\frac{\pi}{3}\), the period is 3.

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Most popular questions from this chapter

Find an equation of the tangent function with period \(2 \pi\) and phase shift \(\frac{\pi}{2}\)

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