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 sin(pi) not equaling 0
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sin(pi) not equaling 0
09212016 03:36 PM
when I type in different values of sin(k*pi) my calculator returns very small numbers instead of 0. How do I fix this?
09212016 06:08 PM
Note that there are four pages of home settings. Tap to display the second page. This page has settings for
font size, calculator name, output display format, menu item format, time, date, color theme, and shading color.
Refer the following link for more details:
http://www.hp.com/unitedstates/calculator/HP_Prime_Quick_Start_Guide_EN_2015.pdf
Regards,
Vidya
Make it easier for other people to find solutions, by marking my answer “Accept as Solution” if it solves your problem.
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09212016 09:51 PM  edited 09222016 06:05 AM
Hi!, @amondellio:
Welcome, to Forum !.
Try, with ... Y=SIN(3.1415............)
With, Apps SOLVE ...
Now, press Num ...
Now, with ... Y=SIN(K*PI)
Press, Num ...
If you put, the value for K, example ... 12, move bar to Y and press Solve, you obtein ... 2.24811...........
Have a nice day !.
@Maké (Technical Advisor Premium  HP Program Top Contributor).
Provost in HP Spanish Public Forum ... https://h30467.www3.hp.com/
09212016 11:23 PM
Hello,
If you type it in the CAS, you will get 0 as the cas works symbolicaly and interprets PI as an exact symboic constant.
In home, PI is a placefolder for the value of PI approximated to 12 digits. So, typing sin(PI) is exactly like typing sin(3.14159265359) and since 3.14159265359 is not exactly pi, sin of it is not exactly 0.
Cyrille
11022017 03:41 AM
This is not an acceptable solution. Why do I need to go to CAS to get the real and correct result for sin(pi)? I understand that HP is using an approximated value of PI in nonCAS, but every other simple nonCAS calculator can still evaluate sin(pi) correctly.
There is a difference if I am typing:
sin(3.13159000) = 2.067...E13 (this is acceptable)
or
sin(pi) = 2.067...E13 (this is not acceptable)
If pi is used inside a trig function in CAS or nonCAS, it should be handled correctly. If I do something like
pi*7/13
then it is ok to use an approximation for pi.
I don't want to switch just to CAS to get correct results for my calculations, I also want them to be correct and exact and "accurate" in nonCAS as far it is possible.
11022017 07:02 AM
Hi,
HOME = numerical
CAS = symbolic
Getting a nonzero result for sin(pi) on any numerical device is an acceptable solution, as PI cannot be accurately represented in any numerical form. Any numerical device that returns 0 is using some means to round the result to what the user expects.
I have tried one of those calculators that give sin(pi) as 0:
I press PI, display shows 3.14159265359 then press SIN and answer is 0
Now I manually type 3.14159265359 then press SIN and answer is 2.067...E13
Why is this calculator giving 2 different answers for what seems to be the same entry? Can I trust a calculator that gives different results for the same apparent entry?
Now when the symbol PI is used, we actually want the exact solution. As PI can never be exactly represented numerically, we have to use a symbolic solver  that is where CAS comes in.
It comes down to using the right tool for the job.
You want a calculator that gives "exact" answers when it's using a numerical solver. This involves tricks to get the expected answer (e.g. hidden extra digits), but how do we know these tricks won't trip us up in other ways?
You might be happy with the "tricks" approach, but I'd rather be in charge myself of what accuracy I want and that determines what tool I use.
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