Draw a right triangle with the right or (0.5π-radian) angle at your bottom-right.
Assign the hypotenuse (or side opposite the right angle) a length of 1 unit.
Label the angle at your bottom-left as θ or Theta; this is the angle equal to
sin-1 x. For sin-1 x to have a sine of x, the side opposite θ
must have a length of x to give sin θ as x/1 or x.
Then to force agreement with the Pythagorean Theorem, the remaining or
third side must have a length of (1 − x2)0.5 so that [(1 − x2)0.5]2 + x2 will
reduce to 12 or 1.
Finally, the tangent of θ radians (where θ = sin-1 x) or tan(arcsin x) will be the
ratio of x to (1 - x2)^0.5 or x/√(1 - x2).
