Answer
$\dfrac{5}{13}$
Work Step by Step
Let us substitute
$f(h^{-1} (\dfrac{5}{12}))=\sin [\tan^{-1}(\dfrac{5}{12})]$
Suppose that $\theta=\tan^{-1} (\dfrac{5}{12})$
Because we know the opposite side and the side adjacent to the angle, it makes sense for us to use the the tangent function:
$\tan {\theta}=\dfrac{opposite}{Adjacent}=\dfrac{5}{12}$
We wish to find the sine function, which can be written as : $\sin (\theta)=\dfrac{opposite}{hypotenuse}$. So, we need to take the help of the Pythagorean Theorem for a right triangle to find the hypotenuse
$=\sqrt{(12)^2+(5)^2}=\sqrt {169}=13$
So, $\sin (\theta)=\dfrac{opposite}{hypotenuse}=\dfrac{5}{13}$
Thus, $\sin [\tan^{-1}(\dfrac{5}{12})]=\dfrac{5}{13}$
