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

1 Answer
Sep 17, 2015

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