thapyhap
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Homework Statement
I want to find the PDF for arccos and arcsin of a uniform random number. Given:
<br /> Y\sim\mathcal{U}(0,2\pi) \\<br /> X = cos(Y)<br />
The Attempt at a Solution
I started with trying to find the CDF:
<br /> \begin{align}<br /> F_X& = P(X \le x) \\<br /> & = P(cos(Y) \le x) \\<br /> & = P(Y \le arccos(x))<br /> \end{align}<br />
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.