root (a-asin(x) = cos(x) ? or what?

Question

Can you explain whats going on here? is it some trig identity i dont know or something else?

Answer 1

Factor $R^2$ and note that

$$1- \sin ^2 (x) = \cos ^2 (x).$$

Answer 2

Try this:

$ \sqrt{R^2-R^2(\sin\theta)^2} = \sqrt{R^2(1-\sin^2 \theta)} $

And because

$ 1-\sin^2 (\theta) = \cos^2 (\theta) $

You can get

$ \sqrt{R^2\cos^2 (\theta)} = R\cos(\theta) $