What is this graphed function with asymptotes at π/2 and -π/2?

Question

I've come across this function with asymptotes at π/2 and -π/2, which crosses the axis at y=1. It doesn't seem to be polynomial or exponential—can anyone figure out what it is?

The asymptotes and y=1 are exact, but the other points I know of are estimates:

-π/2    +∞
-7π/16  5.1000
-3π/8   2.6067
-5π/16  1.7991
-π/4    1.4133
-3π/16  1.2031
-π/8    1.0831
-π/16   1.0200
0       1
π/16    1.0200
π/8     1.0831
3π/16   1.2031  
π/4     1.4133  
5π/16   1.7991  
3π/8    2.6067  
7π/16   5.1000
π/2     +∞

Answer 1

It seems to be the secant function: $$y=\sec(x)$$ where $\sec(x)$ is defined to be $\frac1{\cos(x)}$.