Question

what is the period of the following functions: 2tan(2x)+3

Explanation:

Step1: Recall tangent period formula

The general form of a tangent function is \( y = A\tan(Bx + C)+D \). The period of \( \tan(x) \) is \( \pi \), and for \( \tan(Bx) \), the period is \( \frac{\pi}{|B|} \).

Step2: Identify B in the function

In the function \( y = 2\tan(2x)+3 \), we have \( B = 2 \).

Step3: Calculate the period

Using the period formula for tangent, \( \text{Period}=\frac{\pi}{|B|}=\frac{\pi}{|2|}=\frac{\pi}{2} \).

Answer:

\(\frac{\pi}{2}\)