Re: HP 15C problem (trigs in "C" mode) Message #5 Posted by Karl Schneider on 5 Apr 2007, 12:02 a.m., in response to message #1 by Tom Handy
Tom --
Gerson and Luiz have already answered the question, and provided the remedy. I don't know if you have a manual, but a PDF scan can be purchased on a CD or DVD for a nominal price from this website. A print copy on eBay will cost US$25-35.
Flag 8 set puts the calculator in "Complex mode", in which the input arguments and output results are complex-valued where applicable. It's one of the few things that are not very intuitive on the HP-15C. Flag 8 is testable, allowing user programs to account for results in real and complex mode. Other mode settings -- such as angular measure (DEG/RAD/GRD) or display (FIX/SCI/ENG) -- are not testable on the HP-15C.
So, why is radians mode enforced when Complex mode is set?
Answer: Trigonometric functions are mathematically defined for complex-valued arguments. Their formulae that involve hyperbolic functions, whose arguments must be dimensionless and unscaled (as radians are). For example:
sin (a + ib) = (sin a)*(cos ib) + (cos a)*(sin ib)
= (sin a)*(cosh b) + i*(cos a)*(sinh b)
cos (a + ib) = (cos a)*(cos ib) - (sin a)*(sin ib)
= (cos a)*(cosh b) - i*(sin a)*(sinh b)
Obviously, with b = 0, sine or cosine in complex mode (or these expressions) will produce results identical to sine or cosine in real mode with input in radians, but will take longer to execute.
-- KS
Edited: 9 Apr 2007, 11:00 p.m. after one or more responses were posted
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