Hello GoldenBoy Originally Posted by

**GoldenBoy** well i used the arcsin function and it works relatively well up to arcsin(0.8) in not too many steps. the problem ocurrs at arcsin(0.9) which loses 1º in the conversion and at arcsin(1) (which should be 90º) gives 77.7º or 1.35rads and i cant get passed it.

I even passed the formula to a scientific calculator which accepts equation but no luck.

what am i doing wrong?

Yes, the series converges very slowly as $\displaystyle z \to 1$. So you're best to use the alternative series on that Wikipedia page for $\displaystyle \arctan(z)$:$\displaystyle \arctan(z)=z-\frac{z^3}{3}+\frac{z^5}{5}-...$

and use the formula (above that one on the same page):$\displaystyle \arcsin x = 2\arctan\left(\frac{x}{1+\sqrt{1-x^2}}\right)$

to convert one angle to the other.

I attach a spreadsheet extract showing the comparison between the two methods. Method 1 uses the angle $\displaystyle 0.9$ radians in cell B1, and Method 2 uses the corresponding angle (using the second formula above) $\displaystyle 0.626789$ in cell D1. You'll see that this method converges much more rapidly to the 'correct' answer of $\displaystyle 1.11977...$

Grandad