# Find the period y= \frac{1}{2} \sec x

## Question:

Find the period {eq}y= \frac{1}{2} \sec x {/eq}

## Period of a Secant-Based Function:

When the function incorporates secant in the transformation such as {eq}f(x) = a\sec(k(x+c))+d {/eq}, the period can be found by dividing {eq}2\pi {/eq} by {eq}k {/eq} or {eq}\frac{2\pi}{k} {/eq} because each secant wave repeats itself after a cycle of {eq}2\pi {/eq}.

Given: {eq}y = \frac{1}{2}\sec(x) {/eq}

From the form {eq}f(x) = a\sec(k(x+c))+d {/eq}, the period of the function can be found from the formula {eq}\frac{2\pi}{k} {/eq}. By distribution, it can be seen that the {eq}k {/eq} value in the equation {eq}y = \frac{1}{2}\sec(x) {/eq} is {eq}1 {/eq} since {eq}k {/eq} serves as a coefficient of {eq}x {/eq}.

Therefore, the period:

{eq}\begin{align*} \text{ Period } &= \frac{2\pi}{1} \\ &= 2\pi \\ \end{align*} {/eq}

Therefore, the period of the equation is {eq}2\pi {/eq}.