I want to program a subroutine that randomizes an angle and rotates some coordinates in 3D by that angle. The rotation matrices are already working, so the mathematics are not the problem. I'll have to do that a couple of hundred times to a couple of hundred thousand times, so right now I'm thinking of how to optimize the code. On the one hand I could randomize the sine of the angle and calculate the cosine (both needed for rotation matrices) using the following relation: 
$sine=rand(2)-1;
$cosine=sqrt(1-$sine**2);

[download]
On the other hand I could randomize the angle and calculate both sine and cosine from the angle. 
$angle=rand(2*3.14159);
$sine=sin($angle);
$cosine=cos($angle);

[download]
How can I find out which option is more efficient?

In reply to computational efficiency by thelycaeum

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.