Question

How do you find the exact value of `sec(arccos ((-3/5))`?

Answer 1

`sec(arccos(-3/5)) = -5/3`

Explanation:

Remember that `sec(x) = 1/cos(x)`, so

`sec(arccos(-3/5)) = 1/cos(arccos(-3/5)`

By definition, `cos(arccos(x)) = x`, assuming that `-1 <= x <=1`, since the cosine function can only output values within this range.

So `sec(arccos(-3/5)) = 1/cos(arccos(-3/5)) = 1/(-3/5)`

And that fraction outputs to `-5/3`, so

`sec(arccos(-3/5)) = -5/3`