the graph of $y = \\tan\\left\\frac{1}{4}\\left(x - \\frac{\\pi}{2}\\right)\\right+1$ is shown. what is the…
the graph of $y = \\tan\\left\\frac{1}{4}\\left(x - \\frac{\\pi}{2}\\right)\\right+1$ is shown. what is the period of the function? pi 5pi/2 2pi 4pi
Answer
Explanation:
Step1: Recall tangent - function period formula
The general form of a tangent function is $y = A\tan(B(x - C))+D$, and its period is given by $T=\frac{\pi}{|B|}$.
Step2: Identify the value of B
For the function $y=\tan\left[\frac{1}{4}(x - \frac{\pi}{2})\right]+1$, we have $B = \frac{1}{4}$.
Step3: Calculate the period
Substitute $B=\frac{1}{4}$ into the period formula $T=\frac{\pi}{|B|}$. Then $T=\frac{\pi}{\left|\frac{1}{4}\right|}=4\pi$.
Answer:
$4\pi$