Secant is the reciprocal of cosine.

• zeros: \(\sec (\theta )\) has no zeros, because cosine has no singularities.
• singularities: \(\sec (\theta )\) has a singularity everywhere that \(\cos (\theta )\) has a zero: all of the half-\(\pi \)’s.

This means the graph has no intercepts and there are vertical asymptotes at the half-\(\pi \)’s.

from the ancient Greeks...

Sine, cosine, and tangent come from measurements of the unit circle. What about secant?

In the diagram above, we know that \(a = \cos (\theta )\) and \(b = \sin (\theta )\).

\(a+c\) is the hypotenuse of a right triangle that is similar to the unit circle right triangle. From the point of view of \(\theta \)