Question

in the function f(x) = tan(2x + π), what is the period?
a. $\frac{pi}{3}$
b. $2pi$
c. $\frac{pi}{4}$
d. $\frac{pi}{2}$

Explanation:

Step1: Recall tangent - period formula

The period of the tangent function $y = A\tan(Bx + C)$ is given by $T=\frac{\pi}{|B|}$.

Step2: Identify the value of B

In the function $f(x)=\tan(2x+\pi)$, $B = 2$.

Step3: Calculate the period

Substitute $B = 2$ into the formula $T=\frac{\pi}{|B|}$, we get $T=\frac{\pi}{|2|}=\frac{\pi}{2}$.

Answer:

D. $\frac{\pi}{2}$