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

Explanation:

Step1: Recall secant function definition

The secant function is the reciprocal of the cosine function, so ( y = \sec x=\frac{1}{\cos x} ).

Step2: Recall period of cosine function

The period of ( y = \cos x ) is ( 2\pi ), meaning ( \cos(x + 2\pi)=\cos x ) for all ( x ) in the domain.

Step3: Determine period of secant function

Since ( \sec(x + 2\pi)=\frac{1}{\cos(x + 2\pi)}=\frac{1}{\cos x}=\sec x ), and we check if a smaller positive period exists. The period of ( \cos x ) is ( 2\pi ), and the secant function inherits the period from the cosine function (as it's a reciprocal, and the reciprocal of a function with period ( T ) has period ( T ) if the function is non - zero at the points where the reciprocal is defined). So the period of ( y = \sec x ) is ( 2\pi ), and in the form (?\pi ), the value of (? ) is 2.

Answer:

2