4 batteries vs. 3 batteries
Wes
that a set of batteries should last about 1/3 longer than the 49g+
having only 3 batteries?
For this to be the case, the current in a 50g would have to be about
3/4 as that of a the 49g+.
Can anybody confirm whether or not this is the case?
I get the following readings on my 49g+. (Sorry, the meter's a
RadioShake, not a Fluke)
13.9mA : on
29.5mA : button held down
79.5mA : calculating 400 ! (factorial)
-wes
Avatar_e
so fast? I believe is not a big change, because the "new" hp50g is
more an update from hp49g+ to solve issues than a new product.
I use exhaustively my actual hp49g+, three AAA duracell last as long
5-6 weeks. I hope get at least 8 weeks with another battery (3/4=6/X).
Avatar_e
The Phantom
Here's what I posted back on March 24:
" I made some measurements of the current consumption of the HP49G+ with
standard alkalines installed:
Condition of Current
measurement drain
Calc on, doing nothing 18 mA
Calc on, holding ON down 75 mA
Calc running a program 65 mA
Calc on, pressing RED key 30 mA
Calc on, pressing BLUE key 30 mA"
aplnub
Steen Schmidt
> 79.5mA : calculating 400 ! (factorial)
How did you manage to record the current draw on such a swift
calculation (~0.06 seconds)? Or haven't you installed the ExtraFunc
lib? ;-)
Cheers,
Steen
Wes
> Here's what I posted back on March 24:
> " I made some measurements of the current consumption of the HP49G+ with
> standard alkalines installed:
The batteries I used were not-so-newly-recharged NiMH, so I repeated
the measurements with new standard alkalines, but got nearly the same
results as before:
On, doing nothing - 14.0 mA
On, holding ON down - 78.7mA
On, holding SHIFT - 29.5mA
On, running program - 79.0mA
Off - 0.03mA
The only one where we differed significantly was "running program."
Perhaps it's related to the type of program being run.
-wes
Wes
> How about Caclulator off?
I got about 0.03mA, but this is the lowest range on my meter, so it's 1
significant figure at best. Let's call it 0.02mA - 0.04mA
-wes
Wes
I have bionic eyes. :-)
I have indeed installed ExtraFunc. It's what inspired me to learn how
to automatically get parentheses after function names. Nice piece of
work (though I still use my own ACOT ;-)
-wes
Steen Schmidt
> I have bionic eyes. :-)
Hehe :-)
> I have indeed installed ExtraFunc. It's what inspired me to learn how
> to automatically get parentheses after function names. Nice piece of
> work (though I still use my own ACOT ;-)
Thanks. Oh, the ACOT function. Yes, there is something I need to decide
there...Maybe we should do a poll?
Cheers,
Steen
The Phantom
>How about Caclulator off?
I have two HP49G+'s. The older one draws 29 uA when off and the newer
draws 14 uA when off.
The Phantom
I verified the measurements posted in March. However, since then I got
another HP49G+ with a good keyboard. The newer one draws about 78 mA when
calculating a Singular Value Decomposition, with occasional 1/2 second long
blips up to about 90 mA.
Wes
I guess my original question (electric current in 50g vs. 49g+) doesn't
really depend on the variations introduced by different batteries and
meters. All we need is somebody who has both a 50g and a 49g+ to
measure the current in both machines using the same meter and same
batteries (+1) to see how the currents compare.
I'm just wanting to know if the 4 battery setup will last
proportionally longer than 3.
I guess the real battery test will be testimonies from actual users in
a few weeks. How long does a set last on a 50g compared to similar use
on a 49g+. (I suspect people will be playing with their new toy^H^H^H
calculator more than usual, so the first set of batteries might not be
a fair test.)
-wes
Wes
> there...Maybe we should do a poll?
Depends what you poll. If you poll textbooks, I think you'll get one
result. If you poll people, you'll get, "I never use that function
anyway." ;-)
I wonder how many people have ever used ACOT outside their classroom
experience.
-wes
Steen Schmidt
> I wonder how many people have ever used ACOT outside their classroom
> experience.
My feeling is that the three "other" trig functions (COT, SEC & CSC)
are slightly more used in the States, while in Europe and Asia SIN, COS
& TAN are the heavier used trig functions.
Personally I have never used either of the three (nor their inverses or
their hyperbolic cousins). I included them in the ExtraFunc lib because
TI has them and because someone sometimes complain they aren't there
(for completeness sake I guess :-)
Regards
Steen
torbjorn.ekstrom
Hmm... outside school...
Hyperbolic uses on transmissions theory and I use hyperbolic time to
time to calculate PI and T attenuator beside of arithmetic methode and
this way also can handle attenuator for complex source and loads in
RF-design. (often used in simulators and transmission line software just
depend of complex load handling capability)
Is really irritating in this case hp33s not can handle hyperbolic with
complex numbers, is so easy to handle in hp42s...
Wes
> I included them in the ExtraFunc lib because
> TI has them and because someone sometimes complain they aren't there
> (for completeness sake I guess :-)
For what it's worth, TI calcs also use 0<y<pi for ACOT's range.
Wes
> Steen Schmidt wrote:
> > Personally I have never used either of the three (nor their inverses or
> > their hyperbolic cousins).
> Hyperbolic uses on transmissions theory and I use hyperbolic time to
The reference was not to hyperbolic functions in general, but to the
"other" three trig/hyper functions that are less frequently used:
SEC, CSC, COT, ASEC, ACSC, ACOT
SECH, CSCH, COTH, ASECH, ACSCH, ACOTH
We teach them in school, but I think outside the classroom, people
would be more likely to just use SIN, COS, TAN, SINH, COSH, TANH, and
their inverses.
Is this the case in transmissions theory?
-wes
Wes
> I included them in the ExtraFunc lib because
> TI has them and because someone sometimes complain they aren't there
> (for completeness sake I guess :-)
The TI-89/92+ originally did not have these extra functions. They were
added later in a ROM upgrade. I guess users must have been asking for
them. It does make it easier when teaching/learning these functions to
have them on the calculator.
aplnub
by looking in a chart number by number. Calculators were not allowed,
period. That may have been overkill but man, I know my basic trig
functions to this day without hesitation thanks to my highschool
geometry teacher.
Eric
The Phantom
>> I verified the measurements posted in March.
>
>I guess my original question (electric current in 50g vs. 49g+) doesn't
>really depend on the variations introduced by different batteries and
>meters. All we need is somebody who has both a 50g and a 49g+ to
>measure the current in both machines using the same meter and same
>batteries (+1) to see how the currents compare.
>
>I'm just wanting to know if the 4 battery setup will last
>proportionally longer than 3.
Here are the measurements from my new HP50:
Condition of Current
measurement drain
Calc off 28.4 uA
Calc on, doing nothing 14.6 mA
Calc on, holding ON down 82.5 mA
Calc running a program 73.1 mA
Calc on, pressing RED key 25.8 mA
Calc on, pressing BLUE key 25.8 mA
So, you won't get any better battery life.
If the CMOS process used to make the CPU is the same as the HP49G+, one
effect of the extra voltage might be to allow the calculator to be over
clocked with greater reliability, or to even higher frequencies than the
HP49G+.
Steen Schmidt
> If the CMOS process used to make the CPU is the same as the HP49G+,
It's the same CPU, so this is of course the same as on the HP49G+.
> one effect of the extra voltage might be to allow the calculator to
> be over clocked with greater reliability, or to even higher
> frequencies than the HP49G+.
The CPU isn't affected by the change from 4.5 to 6 VDC - it's run off a
voltage regulator as is always the case with batteries.
Regards
Steen
The Phantom
Snip
>The CPU isn't affected by the change from 4.5 to 6 VDC - it's run off a
>voltage regulator as is always the case with batteries.
Are you suggesting by the phrase, "...it's run off a
voltage regulator as is always the case with batteries.", that all battery
operated calculators regulate the battery voltage before applying it to the
CPU?
>
>Regards
>Steen
Paul Schlyter
regulated power (whether on batteries or not) is very common.
--
----------------------------------------------------------------
Paul Schlyter, Grev Turegatan 40, SE-114 38 Stockholm, SWEDEN
e-mail: pausch at stockholm dot bostream dot se
WWW: http://stjarnhimlen.se/
The Phantom
>> I verified the measurements posted in March.
>
>I guess my original question (electric current in 50g vs. 49g+) doesn't
>really depend on the variations introduced by different batteries and
>meters. All we need is somebody who has both a 50g and a 49g+ to
>measure the current in both machines using the same meter and same
>batteries (+1) to see how the currents compare.
>
>I'm just wanting to know if the 4 battery setup will last
>proportionally longer than 3.
I ran some more tests. I used a variable bench power supply to run 3
calculators, and reduced the voltage until the low battery indicator came
on in the display. These are the results.
Calculator Total voltage when Per cell voltage when
low batt came on low batt came on
HP-48G 3.20 volts 1.067 volts
HP-49G+ 3.45 volts 1.15 volts
HP-50G 4.85 volts 1.2125 volts
If you replace your batteries when the low battery indicator first comes
on, the HP-50G will have significantly shorter run time.
See the discharge characteristic at:
http://data.energizer.com/PDFs/E92.pdf
and you will see that if you only discharge to 1.2125 volts per cell, you
will have used less than half the energy in the cell. Also, note that the
HP-48G in allowing the cell voltage to drop to 1.067 volts has used about
85% of the energy in the cell. (These are eyeball estimates)
Wes
Thanks for reporting your measurements. The following three
measurements aren't quite inversely proportional to the number of
batteries, so they're not as low as I'd hoped, but they're at least
lower
50g
> Calc on, doing nothing 14.6 mA
> Calc on, pressing RED key 25.8 mA
> Calc on, pressing BLUE key 25.8 mA
compared to your original 49g+ measurements
49g+
> Calc on, doing nothing 18 mA
> Calc on, pressing RED key 30 mA
> Calc on, pressing BLUE key 30 mA
But the following two don't make any sense. Why should the current be
HIGHER? I would have thought that the voltage regulator would maintain
the same power consumption as the 49g+, so higher voltage would result
in lower current. Apparently, this is not the case.
50g
> Calc on, holding ON down 82.5 mA
> Calc running a program 73.1 mA
49g+
> Calc on, holding ON down 75 mA
> Calc running a program 65 mA
According to this, if you're running programs most of the time, you'll
have a shorter battery life on a 50g with 4 batteries than on a 49g+
with 3 batteries. How can this be?
-wes
The Phantom
The variation in the current consumption is what I would expect from
calculator to calculator. I have two 49G+'s, and there is almost that much
variation even though they are the same calculator. This is normal
manufacturing variation.
That the 50G and 49G+ numbers are so close tells me that the CPU's are
probably running on the same voltage.
Linear voltage regulators just drop the excess voltage. They don't
maintain a constant *power* drain if the input voltage is raised; they
maintain a constant *current* drain as the input voltage varies. To
maintain a constant *power* drain (which would be a lower *current* drain
in this case) for a higher input voltage to the regulator would require a
switching regulator, and apparently they didn't do that.
I just now hooked the 50G back up to the variable bench supply and
measured the current drain as I varied the voltage from 4.5 volts to 6.5
volts. The current drain didn't vary as the input voltage varied, a sure
sign that they aren't using a switcher.
But what they did do that really hurts battery life, was to set the low
battery indication at 1.2125 volts. As I said:
"...if you only discharge to 1.2125 volts per cell, you
will have used less than half the energy in the cell."
If you replace the batteries when the low battery indicator comes on, you
*will* have a shorter battery life in the 50G. But, since the current is
*nominally* the same, if you monitor the battery voltage with an external
voltmeter and change the batteries when the per cell voltage is 1.15 volts
(as in the 49G+) you will get the same battery life as the 49G+. This
assumes that the 50G+ keeps on working with a voltage that low.
I assume that there is some leeway when the low battery indicator comes
on, but I don't know just how much it might be.
John H Meyers
> if you monitor the battery voltage with an external voltmeter
> and change the batteries when the per cell voltage is 1.15 volts
> (as in the 49G+) you will get the same battery life as the 49G+
> This assumes that the 50G+ keeps on working with a voltage that low.
Since the 50G has four cells in series, whereas the 49G+ has only three,
it could theoretically be possible to run the batteries down
to a lower per-cell voltage before the "battery pack" as a *whole*
dropped to exactly the same final voltage -- provided that
all else was identical in the electronics
(which is probably not the case).
There must have been some better reason for adding an extra cell,
however, which might have been to raise the operating voltage a bit
(would that have a value?), in which case you could not just
run the batteries down quite that low.
So who is the "Dave Arnett" of the ARM-based calculator series,
and why isn't (s)he not speaking for HP now,
the way Dave used not to do? ;-)
[r->] [OFF]
casati
Could it be, that the only reason for 4 - instead of 3 - batteries in
the 50G (and some other new calcs by HP) is, that a battery-pack you
buy at your supermarket contains 4 batteries too?
I was glad to hear the 4 battery news, because in the past I had
problems to track my inventory of eventually different brands of
batteries left over ...
Beste regards,
Peter G.
John Gustaf Stebbins
dogs. Finally solving the buns in half dozen to a pack dilemma.
-j<g>s
"casati" <gebha...@web.de> wrote in message
news:1155403847.1...@74g2000cwt.googlegroups.com...
aplnub
findings?
So HP stuck an extra battery in the thing and then overlooked this?
Weird.
horsz...@gmail.com
when the calculator simply shuts down?
Thanks
Luis
The Phantom
>May I suggest one more test and that is what is the battery voltage
>when the calculator simply shuts down?
>
>Thanks
>
>Luis
Well, I thought about doing that, but I hadn't backed up the calc at the time.
I'll have to back it up and then I'll give it a try.
The Phantom
>May I suggest one more test and that is what is the battery voltage
>when the calculator simply shuts down?
>
>Thanks
>
>Luis
I performed this test on the HP-50 and on an HP-49G+:
Calculator Total voltage when Per cell voltage when
calculator crashed calculator crashed
HP49G+ 3.10 1.033
HP50G 3.65 0.9125
Maybe the low batt indicator comes on so soon on the HP-50 because they
need more voltage for the RS-232? The HP-50 will continue to operate for
quite a while after the low batt indicator comes on, but how will you know
when the per cell voltage reaches about 1.0 volts per cell, which would be
a reasonable point to replace the batteries? If you don't need to use the
RS-232, you could mentally make note of how much usage you've had when the
indicator first comes on, and then use it (the HP-50) for that much again.
(As I noted in another post, the batteries are only about half discharged
when the low batt indicator first comes on.)
These measurements are for *my* calculators only, and there may be a
fairly large variance in the behavior of a large sample of units.
Perhaps a few other people could try this and give us some more data
points.
By the way, I was turning the voltage up and down a number of times and
crashed the calculator quite a few times, but I never did lose the contents
of memory. Some of the settings, such as display resolution, were reset to
the default, but I saw no memory loss.
TW
> need more voltage for the RS-232? The HP-50 will continue to operate for
> quite a while after the low batt indicator comes on, but how will you know
> when the per cell voltage reaches about 1.0 volts per cell, which would be
> a reasonable point to replace the batteries?
More thank likely someone forgot to make all the changes for 4
batteries. When the low battery message comes on, all IO is turned
off. This is definitely a problem that needs to be fixed.
TW
John H Meyers
> By the way, I was turning the voltage up and down a number of times and
> crashed the calculator quite a few times, but I never did lose the contents
> of memory. Some of the settings, such as display resolution, were reset to
> the default, but I saw no memory loss.
Is this thanks to the extra 3v. memory backup cell?
Were "lost" settings due to a restart and/or your STARTUP?
[r->] [OFF]
John H Meyers
> More than likely someone forgot to make all the changes for 4
> batteries. When the low battery message comes on, all I/O is
> turned off. This is definitely a problem that needs to be fixed.
At least it's no problem if the USB cable is in use
which is one I/O which now can't be turned off.
[r->] [OFF]
The Phantom
wrote:
>On Sat, 19 Aug 2006 00:16:08 -0500:
>
>> By the way, I was turning the voltage up and down a number of times and
>> crashed the calculator quite a few times, but I never did lose the contents
>> of memory. Some of the settings, such as display resolution, were reset to
>> the default, but I saw no memory loss.
>
>Is this thanks to the extra 3v. memory backup cell?
That's what I assume.
>
>Were "lost" settings due to a restart and/or your STARTUP?
I have no STARTUP of my own, so restart (of which there were several) must be
the cause.
>
>[r->] [OFF]
horsz...@gmail.com
indicator comes on immediatelly when turning on the machine (when you
turn off the machine, the battery voltage rises so that when you turn
it back on the low bat indicator does not come on immediately unless
the batteries are very weak). I never had problems with corrupted data
when running the batteries till the calculator crashed, and don't
forget you got the CR2032 to help out.
Another trick that will get the last drop of juice from your batteries
is to change only two at a time.
Just some thoughts;
Luis
The Phantom
>I would generally only change the batteries if the low battery
>indicator comes on immediatelly when turning on the machine (when you
>turn off the machine, the battery voltage rises so that when you turn
>it back on the low bat indicator does not come on immediately unless
>the batteries are very weak).
Part of what we can learn from the measurements I made is that the HP-50 low
battery indicator comes on immediately when the batteries are *not* very weak
(only half discharged, in fact). The HP-48G and HP-49G+ behave much more like
what you describe, but even the HP-49G+ isn't as good as the HP-48G at getting
most of the life out of the batteries before the indicator comes on.
James M. Prange
<snip>
> Another trick that will get the last drop of juice from your batteries
> is to change only two at a time.
Perhaps so, but that strikes me as a bad idea.
First off, you'll have one low cell with two fresh cells, so the
total battery voltage will go low while two of the cells are
relatively fresh. Okay, so then you could change only the lowest
cell, so you have two relatively low cells and one fresh cell, but
it seems to me like too much messing around with checking which
cell(s) to change each time.
Much worse, with two fresh cells and one low cell (in series), you
may well end discharging the lowest cell to a very low state, or
even to reverse polarity, with a high danger of leaking its
chemicals, particularly if you don't turn the calculator on very
often (there is still some battery drain even when turned off).
I'd rather avoid damaging my calculator, and perhaps "use up" the
"low" cells in some other device, such as a cheap flashlight.
In my opinion, the best bet is to treat the cells as a matched
set, replacing all of them at the same time, and preferably all
of the same type, brand, and state of charge.
<snip>
> The Phantom wrote:
>> On 13 Aug 2006 14:51:10 -0700, horsz...@gmail.com wrote:
>>
>>> May I suggest one more test and that is what is the battery voltage
>>> when the calculator simply shuts down?
>>>
>>> Thanks
>>>
>>> Luis
>> I performed this test on the HP-50 and on an HP-49G+:
>>
>> Calculator Total voltage when Per cell voltage when
>> calculator crashed calculator crashed
>>
>> HP49G+ 3.10 1.033
>>
>> HP50G 3.65 0.9125
So, although the low battery indicator turns on with a higher
total and per cell voltage, the 50g will continue to operate to a
lower per cell voltage than the 49g+, although it requires a
higher total voltage.
I wonder whether the setting for when the low battery indicator
comes on is in (flashable) ROM, or is it in hardware or "boot
ROM"?
Note that in general, communications, particularly via IR,
require more power, although with the 50g, this shouldn't apply to
USB communications (assuming that the USB host is able to supply
power). Writing to flash memory seems to require the most power.
>> Maybe the low batt indicator comes on so soon on the HP-50 because they
>> need more voltage for the RS-232?
I rather doubt that, as I understand that the "RS-232" on the 50g
is actually a serial port using TTL (3.3V) signal levels, not
actual RS-232 levels.
> The HP-50 will continue to operate for
>> quite a while after the low batt indicator comes on, but how will you know
>> when the per cell voltage reaches about 1.0 volts per cell, which would be
>> a reasonable point to replace the batteries? If you don't need to use the
>> RS-232, you could mentally make note of how much usage you've had when the
>> indicator first comes on, and then use it (the HP-50) for that much again.
>> (As I noted in another post, the batteries are only about half discharged
>> when the low batt indicator first comes on.)
I don't know for sure about the 50g, but with the 49g+, ON&F gets
me some system tests which include "8.POWER". Pressing "8" gets me
to a screen which seems to include a "battery condition" encoded
like "0X0000036B". Presumably, one could note how low this value
can go before the calculator turns off. Note that getting out of
this test entails a warmstart, thus clearing the stack (among
other things).
>> These measurements are for *my* calculators only, and there may be a
>> fairly large variance in the behavior of a large sample of units.
That could be.
<snip>
>>> The Phantom wrote:
<snip>
>>>> I ran some more tests. I used a variable bench power supply to run 3
>>>> calculators, and reduced the voltage until the low battery indicator came
>>>> on in the display. These are the results.
>>>>
>>>> Calculator Total voltage when Per cell voltage when
>>>> low batt came on low batt came on
>>>>
>>>> HP-48G 3.20 volts 1.067 volts
>>>> HP-49G+ 3.45 volts 1.15 volts
>>>> HP-50G 4.85 volts 1.2125 volts
Has anyone tried using NiMH (or NiCAD) cells in a 50g yet?
<snip>
--
Regards,
James
Joe Horn
> Has anyone tried using NiMH (or NiCAD) cells in a 50g yet?
That's all I use, having killed the included alkalines long ago. I use
1000 mAh cells from http://www.amondotech.com/ They work great.
-Joe-
John H Meyers
to recharge more often (to suppress "low batt"),
or else run until a crash (in a pinch),
but you won't need to spend any more.
If anyone makes a charger using the new serial port,
then perhaps you'll never need to change batteries
(over an extremely long time, anyway).
[r->] [OFF]
The Phantom
The high turn-on voltage for the low battery indicator on the HP50 may be
a good thing when using NiMH or NiCAD batteries.
http://data.energizer.com/PDFs/nh12-850.pdf
If the low battery indicator turned on at slightly more than 1 volt per
cell (which is good when using alkalines), the NiMH cells would be on a
very steep part of the discharge curve, only minutes away from exhaustion.
But the HP50's low battery indicator comes on at 1.2125 volts per cell
(my HP50 does so; I don't know about any others). Eyeballing the NiMH
discharge curve, this looks to me like the cells would be about 70%
discharged, so there is ample time to change them.
Veli-Pekka Nousiainen
X
> The high turn-on voltage for the low battery indicator on the HP50
> may be a good thing when using NiMH or NiCAD batteries.
>
> http://data.energizer.com/PDFs/nh12-850.pdf
>
> If the low battery indicator turned on at slightly more than 1 volt
> per cell (which is good when using alkalines), the NiMH cells would
> be on a very steep part of the discharge curve, only minutes away
> from exhaustion.
>
> But the HP50's low battery indicator comes on at 1.2125 volts per
> cell (my HP50 does so; I don't know about any others). Eyeballing
> the NiMH discharge curve, this looks to me like the cells would be
> about 70% discharged, so there is ample time to change them.
Hurrah!
I'm mostly using NiMH
and the new 59G will make that much more easier
now that the LowBat has this new feature
BUT
perhaps user could have a flag to set it 1_V <--> 1.2_V
or NiMH <--> Alcaline
or
->VOLTAGE VOLTAGE->
commands setting your own desired level
similar to the keybounce time setting
???
Veli-Pekka Nousiainen
> Wes wrote:
>
>> I wonder how many people have ever used ACOT outside their classroom
>> experience.
>
> My feeling is that the three "other" trig functions (COT, SEC & CSC)
> are slightly more used in the States, while in Europe and Asia SIN,
> COS & TAN are the heavier used trig functions.
>
> Personally I have never used either of the three (nor their inverses
> or their hyperbolic cousins). I included them in the ExtraFunc lib
> because TI has them and because someone sometimes complain they
> aren't there (for completeness sake I guess :-)
Me for sure - I hate that HPQ left these analytic functions out
(A)CSC[H], (A)SEC[H], (A)COT[H]
I would like to see CAS Commands supporting them, too
I mean that one write equivalents for these:
ACOS2S, ASIN2C, ASIN2T, ATAN2S, HALFTAN, SINCOS,
TAN2CS2, TAN2SC2, TRIGCOS, TRIGSIN, TRIGTAN,
ProductLog or is that Lambert W
http://documents.wolfram.com/v5/Built-inFunctions/MathematicalFunctions/InverseFunctions/FurtherExamples/ProductLog.html
James M. Prange
> Wes wrote:
>
>> I wonder how many people have ever used ACOT outside their classroom
>> experience.
>
> My feeling is that the three "other" trig functions (COT, SEC & CSC)
> are slightly more used in the States, while in Europe and Asia SIN, COS
> & TAN are the heavier used trig functions.
Way back when I took trig in high school, we used printed tables
with pencil and paper. Since it's generally considered easier to
multiply than to work out a long division problem, we were taught
to prefer a function that requires a multiplication over one that
requires a division, for example, multiply by the cotangent rather
than divide by the tangent.
Granted, with a calculator, division is just as easy as
multiplication, but I still tend to, for example, think of
multiplying by the cotangent, so press TAN and then 1/x and then
multiply, although I know that I could save a keypress by pressing
TAN and then divide.
> Personally I have never used either of the three (nor their inverses or
> their hyperbolic cousins). I included them in the ExtraFunc lib because
> TI has them and because someone sometimes complain they aren't there
> (for completeness sake I guess :-)
Well, I find them very useful. Thanks for including them.
Maybe I should add that the calculus textbooks that I've seen make
heavy use these "extra" functions.
--
Regards,
James