Question

How do you calculate `cos(tan^-1 (-12 / 5))`?

Answer 1

If you have a graphing calculator, you can simply punch in the equation.
I am using the TI-84 Plus with it in 'degree mode'

When I put in
The equation listed above I got the answer of .3846153846
Which would be rounded to .385 or .38 degrees.

Answer 2

A triangle with sides `5`, `12` and `13` is a right angled triangle, since `5^2 + 12^2 = 25 + 144 = 169 = 13^2`.

Let us use `theta` to denote the (second largest) angle between the side of length `5` and the hypotenuse - which has length `13`.

Then `tan theta = 12/5` and `cos theta = 12/13`

`tan (-theta) = -tan theta = -12/5`

So `tan^(-1)(-12/5) = -theta`

and `cos(tan^(-1)(-12/5)) = cos(-theta) = cos(theta) = 12/13`