Question

How do I find the value of `sec(-pi)`?

Answer 1

`sec(-pi) = -1`

Explanation:

Using a unit circle in standard position,
the angle `(-pi)` is a semicircle with its terminal point on the negative X-axis (at `(x,y) = -1,0`)

The length of the hypotenuse will be
`color(white)("XXX")sqrt((-1)^2+0^2) = 1`

and since the definition of `sec` is
`color(white)("XXX")sec = ("hypotenuse")/("x-coordinate")` (of unit circle)

`sec(-pi) = 1/(-1) = -1`