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

2 Answers
Aug 29, 2015

Answer:

#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

Answer:

#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)#