Question

what is the period of the function y = sec x? ?π

Explanation:

Step1: Recall the definition of secant function

The secant function is defined as $\sec x=\frac{1}{\cos x}$.

Step2: Recall the period of cosine function

The period of the cosine function $y = \cos x$ is $2\pi$, which means $\cos(x + 2\pi)=\cos x$ for all $x$.

Step3: Determine the period of secant function

Since $\sec(x + 2\pi)=\frac{1}{\cos(x + 2\pi)}=\frac{1}{\cos x}=\sec x$, and we can check that there is no smaller positive number $T$ (where $T< 2\pi$) such that $\sec(x + T)=\sec x$ for all $x$ (because the period of $\cos x$ is $2\pi$ and $\sec x$ is the reciprocal of $\cos x$), so the period of $y = \sec x$ is $2\pi$. In the form of $?\pi$, the value of $?$ is $2$.

Answer:

2