Posted by Soroban on September 13, 2002 at 13:42:59:
In Reply to: Sinh - sin -Sinh - sin posted by Pi on September 13, 2002 at 08:03:56:
: Can anyone offer me a proof that...
: sin(ix) = isinh(x)
Since you are working sinh(x), I assume you know
the infinite series
for sin(x) and sinh(x). [If I'm wrong - sorry!]
Substitute ix into the sine series:
sin(ix) = (ix) - (ix)^3/3! + (ix)^5/5! - (ix)^7/7! + ...
= i[x + x^3/3! + x^5/5! + x^7/7! + ...]
= i sinh(x)
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