Question

How do I find the approximate value?

Answer 1

\[\tan (\cos^{-1} 12/13)\]

Answer 2

You can do better than the approximate value. We'll find the exact value.
Hint:

The following triangle is right-angled, since 5^2+12^2=13^2.
from \(\cos^{-1}(12/13)\), you can find (from the triangle) which angle is theta.
From there on, you can find \(\tan(\theta)\).

Answer 3

I'm still confused on how to find which angle is theta

Answer 4

that is a pretty good question
what exactly are you supposed to find?

Answer 5

oh this
\[\tan (\cos^{-1} 12/13)\]
picture gives it to you
write the tangent of the angle in the triangle above
the angles whose cosine is \(\frac{12}{13}\)