Question

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

Answer 1

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

Answer 2

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

Answer 3

now that is a different story

Answer 4

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

Answer 5

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

Answer 6

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
\[f^{-1}(f(x)) \stackrel{*}{=} x\]

Answer 7

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