|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
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.
Edited: 9 Apr 2007, 11:00 p.m. after one or more responses were posted