Question

Tan (sin^-1(-1))=____?
A. undefined
B. -1
C. 1
D. 0

Answer 1

Wait is it A. undefined ?

Answer 2

What you put into a trig function is an angle and out of it you get a ratio of sides. So the inverse of a trig function takes ratios of sides and gives you an angle! To make our lives simpler, I will do that:

\[\tan ( \sin^{-1}(-1))\]

See, that arcsine in there is giving us an angle:

\[\theta = \sin^{-1}(-1)\]
We can turn it inside out by taking sine of both sides:

\[\sin(\theta) = -1\]

So now what value of \(\theta\) gives us this answer? Once you figure this out you can plug it in based on our substitution to find out what


\[\tan ( \sin^{-1}(-1)) = \tan(\theta)=?\]