Question #bff37

1 Answer
Jan 9, 2018

#24/7#

Explanation:

The answer to this question isn't an angle, it's a ratio, so it's not really in radians, but:

Start with:

#tan^(-1)(x) =sin^(-1)(24/25)#

Take the tangent of both sides:

#tan(tan^(-1)(x)) =tan(sin^(-1)(24/25))#

The left hand side is a composition of a function and its inverse, so #tan(tan^(-1)(x))=x#:

#x=tan(sin^(-1)(24/25))#

let #theta =sin^(-1)(24/25)#, we're trying to find #tan(theta)#.

We know that #sin(theta) = 24/25#, so opposite #theta# is 24, the hypotenuse is #25#, and therefore the side adjacent to #theta# is 7 by Pythagorean triples.

Since opposite is 24 and adjacent is 7, we know that #tan(theta) = 24/7#