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

2 Answers
Aug 29, 2015

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)

Aug 29, 2015

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:enter image source here
from which it follows:
tan(sin^(-1)(2/3)) = +- 2/sqrt(5) = +- 2/5sqrt(5)