Tan(tan^-1 7/3)
Find the exact value

Question

Tan(tan^-1 7/3) 
Find the exact value

anonymous · Answer

my guess is $\frac{7}{3}$ since this is like "who is buried in grant's tomb"
you are composing a function with its inverse
you always get the input back

anonymous · Answer

Another example is 
Sin^-1 (sin11pi/5)
@satellite73

anonymous · Answer

now that is a different story

anonymous · Answer

the answer CANNOT  be $\frac{11\pi}{5}$ because the range of arcsine is $[-\frac{\pi}{2},\frac{\pi}{2}]$

anonymous · Answer

subtract $2\pi$ from your input to give you the correct answer

rational · Answer

For trig functions I think below is always true
$$f(f^{-1}(x)) = x$$

But below wont work if $x$ is not in the domain of inverse
$$f^{-1}(f(x)) \stackrel{*}{=} x$$

anonymous · Answer

How much would I be subtracting? I don't how much 2pi would take away