50g Hyperbolic Identity Question

[Bill Triplett]

When doing symbolic math using complex arguments, various different math engines respond to sinh(X + Y*i) by simplifying in terms of trig functions which do not have imaginary arguments. For example, one engine responds with ...

sinh(X) * cos(Y) + cosh(X) * sin(Y) * i

Question: How can we have a HP 50g respond in this way when given sinh(X + Y * i) as input? I know folks are often using the Prime nowadays, but the venerable 50g has a charm of its own.

[Bill Triplett]

If using the HP Prime, we can apply one of Albert Chan's ideas from a different problem:

evalc(sinh(x+y*i))

Result:

-SINH(-RE(x)+IM(y))*COS(IM(x)+RE(y))+i*COSH(-RE(x)+IM(y))*SIN(IM(x)+RE(y))

This works, but it seems as if it was written and authored by the department of redundancy department.

In the Prime, go back to the CAS settings screen, and uncheck "Complex." Then, it responds:

SINH(x)*COS(y)+i*COSH(x)*SIN(y)

All is good for the Prime.

[Massimo Gnerucci]

(08-26-2022 12:57 PM)Bill Triplett Wrote:  the department of redundancy department.

Perfect!