Question

How do you do simplify `cos [sec ^-1 (-5)]`?

Answer 1

`-1/5`

Explanation:

`cos[sec^-1(-5)]`

Finding the value of the Composition:

Lets being to solve the equation by working on the inside. Immediately we can see that `sec^-1(5/(-1))` isn't a special angle. If you noticed how I attached the negative sign to "1" is because sec = `r/x`. The radius can not be negative. and "1" serves as the x-value in this equation.

Note: The inverse of cosine (secant) is restricted between `0 < x < pi`. (This would matter if it were asking for sin instead of cos because the y-value would become negative and give you a wrong answer).

Now cosine is `x/r`. So simply put the values where they belong.

`cos((-1)/5)` = `-1/5`

This is not a special angle so leave the answer as a improper fraction or decimal. Whatever your instructor prefers. :)