Question for Trig Gurus

[Namir]

Based on Gerson's fine comments and math work, I did some curve fitting for asin(x), sinh(x), and the error between the two for 0.5<= x <= 0.9 and I found:

asin(x) = sinh(x) for 0 <= x <= 0.5

The first error correction formula (based on log10(error) vs x:

asin(x) = sinh(x) + 10^(-4.48918286080606 + 3.8564664209301*x)

And a somewhat less accurate formula (based on log10(error) vs log10(x)):

asin(x) = sinh(x) + 10^(-0.770263767622744 + 6.27135730622513*log10(x))

I guess you can use the first approximation even up to x=1.

Also,

acos(x) = pi/2 - asin(x)

and,

atan(x) = tanh(x) for 0 <= x <= 1

Since the Casio FX-10 has the e^x function, I can calculate hyperbolic functions with some reasonable ease.


:-)

Namir