Question

Simplify tan(sin^-1(x)).

Answer 1

is that inverse?

Answer 2

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

Answer 3

I began by letting \[\sin^{-1} (x) = \Theta \]
therefore \[\sin(\Theta) = x\]

I now seek tan(theta)

\[\tan(\Theta) = \frac{ \sin(\Theta) }{ \cos(\Theta) }\]

and here I get stuck.

Answer 4

Work from the inside out.\[\Large \arcsin x=\theta \qquad\to\qquad \sin \theta = \frac{x}{1}\]The reason I wrote it like that, is so we can relate it to the sides of a triangle.
Remember the relationship that sine has with a triangle?

Answer 5

sinx = y/r

Answer 6

or opp/hyp

Answer 7

Yes, but you're thinking too fancy.

Ya there we go :)

Answer 8

So let's set up a triangle! :)

Answer 9

Understand where we're going with this?

Answer 10

I think. The hyp= 1 is the radius of the unit circle, correct?

Answer 11

We don't actually want to relate this back to the unit circle :)
Let's find the missing side of the triangle.

Answer 12

You mean an expression for the bottom side?

\[\sqrt{x ^{2}-1}\]

Answer 13

I think you have that backwards maybe :o