ok, so what about deriving the other ratios from knowing that sine=0.642?

Once you know the sine of an angle, then you can get all the other functions using this famous identity:

Sin^2(x)  +  Cos^2(x) =1. To see how, go online to this link: https://en.wikipedia.org/wiki/Sine

Go down the page to "Other Trigonometric Functions" and look at the first column.

sine  =  y / r  =   .642 / 1         

cosecant =   r / y  =   1 / .642

cosine =   x / r   

Note....  x = sqrt (1 - y^2 )  =    sqrt ( 1 - .642^2) ≈ .7667   

So.....x / r  =  .7667/ 1

secant  =  r / x   =   1 / .7667

tangent  =   y / x  =  .642 / .7667

cotangent  =  x / y  = .7667 / ,642