how many periods of the function y = tan x are there between $\frac{-7pi}{6}$ and $\frac{11pi}{6}$?\n1…

how many periods of the function y = tan x are there between $\frac{-7pi}{6}$ and $\frac{11pi}{6}$?\n1 period\n4 periods\n3 periods\n2 periods

how many periods of the function y = tan x are there between $\frac{-7pi}{6}$ and $\frac{11pi}{6}$?\n1 period\n4 periods\n3 periods\n2 periods

Answer

Explanation:

Step1: Recall the period of tangent function

The period of $y = \tan x$ is $\pi$.

Step2: Calculate the length of the interval

The length of the interval from $x_1=-\frac{7\pi}{6}$ to $x_2 = \frac{11\pi}{6}$ is $L=\frac{11\pi}{6}-\left(-\frac{7\pi}{6}\right)=\frac{11\pi + 7\pi}{6}=\frac{18\pi}{6}=3\pi$.

Step3: Determine the number of periods

Divide the length of the interval by the period of the function. The number of periods $n=\frac{3\pi}{\pi}=3$.

Answer:

3 periods