Question

What is `\cos ^{-1}(.60)`?

Answer 1

`cos^-1 (0.6)= 53.1°`

Explanation:

Note that `cos^-1` does not mean `1/cos` as we are used to in algebra.

`cos^-1` is the notation used for arc-cos.

`Cos 30° = 0.866 " "hArr" "cos^-1(0.866) = 30°`

In this case `cos^-1 (0.60)` is asking the question..

"Which angle has a `Cos` value of 0.60?"

The only way to determine this is with a calculator or tables.
Using a graph is possible, but not accurate enough.

Depending on which calculator you have, the following are possible key presses:

D.A.L. calculators:

shift `cos^-1 (0.6) =" larr` ( ) might not be needed on some models

The answer will be `53.1°`

Or `0.6" shift" cos^-1" "larr =` sign not needed, the answer `color(white)(...............................................)`appears immediately

The answer will be `53.1°`

Note that this is only the acute angle, the 1st quadrant angle.
In the 4th quadrant, `Cos 306.9° = 0.6`