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Calculators Calculator giving weird answers?

  1. Feb 25, 2012 #1
    For sin(4pi), my calculator gives -2^-13.

    Obviously, that is really close to the correct value of 0, but it just says 0 for ANY other multiple of pi I've tried.

    Weird right?

    TI-83 plus.. common calculator. Anyone have issues like this?
  2. jcsd
  3. Feb 25, 2012 #2
    Ha! Just tried it on my TI-83+ (from 1997), and it shows the same thing. Says the same for Sin4pi. Sin6pi returns 2E-13, and sin8pi returns -4E-13.

    My TI-36X Pro, which I use almost exclusively now, returns 0.
  4. Feb 25, 2012 #3
    Yep, I get those same results as you, never tried those, so my capital ANY was not a very meaningful "ANY," heh.

    When it showed this error, I actually decided to graph "sin x" on it, then find the value when x = 4pi.. still returns -2e-13 that way.

  5. Feb 25, 2012 #4


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    Welcome to the joys of floating point arithmetic.
  6. Feb 25, 2012 #5

    jim hardy

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    hmmmm transcendentals likely calculated by a series...

    and 10-13 is about 1/(2^43)

    i'm guessing their internal binary arithmetic is good to ~43 bits.
    Anybody got an old HP31?

    old jim
  7. Feb 25, 2012 #6


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    It must be doing the 4*pi calculation first, incorporates some rounding error, then takes the sin of that.
  8. Feb 25, 2012 #7
    But it works fine for something like pi/2 or even 10pi.
  9. Feb 25, 2012 #8
    Try 8 pi.
  10. Mar 9, 2012 #9
    um, so, I was kind of bored this evening and I saw this thread. Since I love excel and graphs... and numbers, I just started punching multiples of pi into my TI- 83 Plus calculator and noting down the results from 1pi to 100pi.

    I got these graphs

    the first is the whole shebang, the second is a zoom in on the first portion of the graph

    it's interesting I guess, but I don't know enough about calculators to have any idea of why it does it like this. I'm gonna keep going, since I have nothing else to do tonight, and see what happens on out from 100pi.

    also there is the excel file if anyone feels like looking at the numbers and messing with them

    Attached Files:

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