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Chapter 4: Problem 9

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

Short Answer

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

Step by step solution

01

Identify the transformation of the function

First identify the function \(y=2 \tan \frac{x}{2}\) as a transformation of the standard tangent function \(y = \tan(x)\). Here, the coefficient of \(x\) inside the function is \(\frac{1}{2}\), so \(B = \frac{1}{2}\).
02

Calculate the period

Since the period of a transformed function \(y = \tan(Bx)\) is given by \(\pi/B\), substitute \(B = \frac{1}{2}\) into this formula. Thus, the period is \(\pi/\frac{1}{2}\).
03

Simplify the period

Simplify the expression from the previous step: \(\pi/\frac{1}{2} = 2\pi\).

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