Draw a right triangle. The particular shape doesn't matter.
right triangle:
/|
/ |
/ |
/ |
/ |
/ |
/ |
----------------------
By definition, the arccosine returns an angle value. So arccos(x + 1) = @ for some angle @. (I'm using "@" to stand for "theta".) You need to find the tangent of that angle. So let's label the triangle with the angle:
right triangle:
/|
/ |
/ |
/ |
/ |
/ |
/@ |
----------------------
We also know, by definition, that "arccos(x + 1) = @" means that "cos(@) = x + 1". In this case, it will be more useful to express this as "(x + 1)/1", because that gives us our "adjacent" (namely, x + 1) and our "hypotenuse" (namely, 1). So now we have:
right triangle:
/|
/ |
1 / |
/ |
/ |
/ |
/@ |
----------------------
x + 1
Use the Pythagorean Theorem to find the value for "opposite", and then read off the value of the tangent.