What is the period of the function (\sec x)?

Correct answer: (2\pi)

The direct answer is option C, 2π. A period is the smallest positive number T for which f(x+T)=f(x) wherever the function is defined. Since sec x=1/cos x and cos(x+2π)=cos x, we get sec(x+2π)=sec x. A smaller shift, π, changes neither cosine nor secant? Actually cos(x+π)=-cos x, so sec(x+π)=-sec x, not the same function. Thus 2π is the least positive period. Option A, π/π, equals 1 and is not the period. Option B, π/2, changes secant into a different value. Option C works exactly. Option D, 4π, is also a period, but it is not the fundamental or smallest period. Memory cue: secant follows cosine’s period, so remember 2π, not π.