Question

What is the period of `y = 1+ tan((1)/(2)x)`? A. `(1)/(2)` B. π C. 2π D. 1

Answer 1

Answer:

C. $2\pi$

Step-by-step explanation:

We have been given a trigonometric function $y=1+\text{tan}(\frac{1}{2}x)$. We are asked to find period of our given function.

We know that period of a tangent function is form $f(x)=a\cdot \text{tan}(bx)+c$, is $\text{Period}=\frac{\pi}{|b|}$.

We can rewrite our given function as:

$y=\text{tan}(\frac{1}{2}x)+1$

We can see that value of b is $\frac{1}{2}$ for our given function.

$\text{Period}=\frac{\pi}{\frac{1}{2}}$

Using fraction rule $\frac{a}{\frac{b}{c}}=\frac{ac}{b}$, we will get:

$\text{Period}=\frac{2\pi}{1}$

$\text{Period}=2\pi$

Therefore, period of our given function is $2\pi$ and option C is the correct choice.

Answer 2

ANSWER

C. 2π

EXPLANATION

The given function is

$y = 1 + \tan( \frac{1}{2}x )$

The period of the tangent function is given by

$T = \frac{\pi}{ B }$

where B is the coefficient of the argument of the tangent function.

This implies that,

$B = \frac{1}{2}$

Hence, the period of the given function is,

$T = \frac{\pi}{ \frac{1}{2} }$

This simplifies to,

$T = 2\pi$

The correct answer is option C.