Question

How do you evaluate `sec ((3pi) / 2)`?

Answer 1

First of all, recall the definition of `sec`:
`sec(alpha)=1/cos(alpha)`

To determine `cos((3pi)/2)`, recall the definition of `cos` based on a concept of a unit circle:

`cos(alpha)` is an abscissa (X-coordinate) of a point on a unit circle, which radius makes an angle `alpha` with a positive direction of the X-axis, counting from that positive direction of X-axis counter-clockwise.

Angle `(3pi)/2` corresponds to a point with coordinates `(0,-1)` on a unit circle.
Therefore, `cos((3pi)/2)=0`.

Since `sec((3pi)/2)=1/cos((3pi)/2)` and `cos((3pi)/2)=0`, the value of `sec((3pi)/2)` is undefined.