Question 820437
In each case, find sin(a), cos(a), csc(a), sec(a), and cot(a). Note: 'a' means alpha. 
45. cos(2a)=3/5 and 0°<2a<90° 
------
cos = x/r
If cos(2a) = 3/5, x = 3 and r = 5
------
Then y = sqrt[5^2-3^2] = sqrt[16] = 4
------
And sin(2a) = y/r = 4/5
-------
Now use the half-angle formulas to get:
sin(2a/2) = sqrt[(1-cos(2a)/2] = sqrt[(1-(3/5))/2] = sqrt[1/5] = (1/5)sqrt(5)
cos(2a/2) = sqrt[(1+cos(2a)/2] = sqrt[(1+(3/5))/2] = sqrt(4/5) = (2/5)sqrt(5)
----
tan(2a/2) = sin(2a/2)/cos(2a/2) = 1/2
------
Note: csc(a), sec(a), cot(a) are the inverse of above.
===========
Cheers,
Stan H.
===========