- #1

thapyhap

- 8

- 0

## Homework Statement

I want to find the PDF for arccos and arcsin of a uniform random number. Given:

[tex]

Y\sim\mathcal{U}(0,2\pi) \\

X = cos(Y)

[/tex]

## The Attempt at a Solution

I started with trying to find the CDF:

[tex]

\begin{align}

F_X& = P(X \le x) \\

& = P(cos(Y) \le x) \\

& = P(Y \le arccos(x))

\end{align}

[/tex]

But I'm stuck on the next step. I found a similar walkthrough online for arcsin, but I don't understand the step they take at this point either. Any pointers would be appreciated.