Question

How do you calculate `Tan (sin^-1 (2/3))`?

Answer 1

`2/sqrt(5)`

Explanation:

Drawing the right angled triangle, you realise that length of opposite side `=2` and length of hypotenuse `=3 \Rightarrow` length of adjacent side `= sqrt(3^2-2^2)=sqrt(5)`

Thus `tan (sin^-1 (2/3))=(opposite)/(adjacent)=2/sqrt(5)`

Answer 2

`tan(sin^(-1)(2/3)) = +- 2/5sqrt(5)`

Explanation:

If `x = sin^(-1)(2/3)`
then `sin(x) = 2/3`

And we have one of the defining triangles below:
from which it follows:
`tan(sin^(-1)(2/3)) = +- 2/sqrt(5) = +- 2/5sqrt(5)`