(35S) complex asin, acos, atan + hyperbolic

05052017, 07:31 PM
(This post was last modified: 06152017 01:15 PM by Gene.)
Post: #1




(35S) complex asin, acos, atan + hyperbolic
Curiously, the complex sin, cos and tan are available on the HP35s, but not the inverse arc functions.
So, you can find below 3 programs to compute them. They use the labels H, I, J as these letters are placed on the corresponding SIN, COS, TAN keys. The corresponding formulas are: asin(z) = i.ln(i.z+sqrt(1z²)) acos(z) = i.ln(z+sqrt(z²1)) atan(z) = i/2.ln((1i.z)/(1+i.z)) Usage: asin(x): XEQ H acos(x): XEQ I atan(x): XEQ J The variables of the calculator are preserved. The stack is preserved too. LASTx is set with the right previous value before running the programs. (I use the following tip: ABS followed by CLx) Code for asin(x) Code:
Code for acos(x) Code:
Code for atan(x) Code:
To check the code: asin(2) = 1.5708 i 1.3170 acos(2) = 3.1416 i 1.3170 atan(2 i 3) = 1.4099 i 0.2291 For hyperbolic functions: I don't provide code because I don't use them, but you can calculate them easily, either from the exp/logarithmic expressions, or from: sinh(z) = i.sin(i.z) cosh(z) = cos(i.z) tanh(z) = i.tan(i.z) asinh(z) = i.asin(i.z) acosh(z) = i.acos(z) atanh(z) = i.atan(i.z) (I haven't checked the latter expressions myself) 

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