Question 617164
The radical symbol is used for <i>all</i> kinds of roots: square roots, cube roots, 4th roots, etc. So saying "radical 5" is not a correct way to describe whatever it is in your problem. (It is just incorrect to say "root 5".) Please tell us what kind of root it is. If it is a square root, then say "square root of 5" (or just "sqrt(5)".<br>
And what is inside your radical? The 5? of the whole fraction, 5/3? Use parentheses to make things clear. For example sqrt(5)/3 if just the 5 is in the square root and sqrt(5/3) if the whole fraction should be inside the square root.<br>
Please re-post your question in a clear enough way that we can figure out what the problem actually is.<br>
P.S. Now that I know what the problem is...
What we are trying to do is figure out what cos(2A) is when all we have to start with is {{{sin(A) = sqrt(5)/3}}}<br>
There are three variations to the cos(2A) formula:<ul><li>{{{cos^2(A)-sin^2(A)}}}</li><li>{{{2cos^2(A)-1}}}</li><li>{{{1-2sin^2(A)}}}</li></ul>Fortunately, the last one only requires sin(A). So we will use that one:
{{{cos(2A) = 1 - 2sin^2(A) = 1 - 2(sqrt(5)/3)^2 = 1 - 2(5/9) = 1 - 10/9 = 9/9 - 10/9 = -1/9}}}