Question

Question #1364e

Answer 1

`tan(sin^-1(A/2)) = A/sqrt(4 - A^2)`

Explanation:

If we let `theta = sin^-1(A/2)`, then

`sintheta = A/2`

And thus the expression becomes :

`tan(theta)`

Given the value of sine, we can find the value of tangent. We know that the opposite side in the triangle would measure `A` and the hypotenuse `2` because `sintheta = "opposite"/"hypotenuse"`.

It follows that `"adjacent" = sqrt(2^2 - A^2) = sqrt(4 - A^2)`

Thus `tantheta = A/sqrt(4 - A^2)`

Hopefully this helps!