Question

What is `tan(arcsin( 5/6))`?

Answer 1

`tan(arcsin(5/6)) = =+-5/sqrt(11)`

Explanation:

If `x = arcsin(5/6)`
`color(white)("XXXX")`then `sin(x) = 5/6`
and `x` is one of the 2 possible angles indicated below
(arcsin is restricted to `[0,pi]`):

The third side (`+-sqrt(11)`) can be derived using the Pythagorean theorem.

From the diagram:
`color(white)("XXXX")` `tan(x) = +-5/sqrt(11)`