Find the value of sin(arc cos 1/x)?

Question

Could you show me the steps? I really don't understand how to do it.

And I don't think there's supposed to be a set answer like 5 or 3.6533 I think it's going to be something in terms of tan or cos or something... and something I forgot to mention is that x was a substitute for theta

Answer 1

Sketch a right triangle, angle A at the left. since cos A = 1/x, label the side adjacent to A with 1, hypotenuse with x. So side opposite A must be √(x² - 1). A = arc cos 1/x, thus sin A = sin(arc cos 1/x) = [√(x² - 1)]/x