Why is sec(0) = 1?

##sec(0) = 1/cos(0) = 1/1 = 1##

Secant is defined as ##sec(x) = 1/cos(x)## , in other words it means that ##sec(x)## is the reciprocal function of ##cos(x)##.

Here's a graph of ##y=cos(x)##. graph{cos(x) [-10, 10, -5, 5]} We see that ##cos(0) = 1##

Let's get back to our problem. We want to calculate ##sec(0)##.

From the definition above, ##sec(0) = 1/cos(0)## .

Since ##cos(0)=1##, ##sec(0)=1/1=1##

You might want to understand why ##cos(0)=1##, in that case, read this:

You can also learn about the unit circle and the definition of cosine.