math module broken?

[Frank Millman]

Hi all

I was helping my niece with her trigonometry homework last night. Her
calculator's batteries were flat, so I thought I would use Python's
math module to calculate sin, cos, and tan.

I tried the example in the text book first, to ensure that I was
getting the correct result, but it did not agree. Then my wife had the
idea of using the Microsoft calculator in scientific mode, and that
one did give the correct result.

Here are some examples -

sin(32) -
Python 0.55142668
Microsoft 0.52991926

cos(32) -
Python 0.83422336
Microsoft 0.84804809

tan(32) -
Python 0.66100604
Microsoft 0.62486935

Version is Python 2.3.3. I get the same results on Linux and on
Windows 2000. I also get the same results using the cmath module.

Can someone please explain these discrepancies?

Thanks

Frank Millman

[Dan Sommers]

On 23 Jul 2004 23:00:18 -0700,
da*****@yahoo.c om (Dan Bishop) wrote:

da*****@yahoo.c om (Dan Bishop) wrote in message news:<ad******* *************** ****@posting.go ogle.com>...

def mysin(x):
return math.sin(math.r adians(x)) Even better: def mysin(x):
return math.sin(math.r adians(x % 360))

Why?

for x in range( 20 ):

print '%.12f %.12f' % (math.sin( math.radians( x ) ), math.sin( math.radians( x % 360 ) ))

0.000000000000 0.000000000000
0.017452406437 0.017452406437
0.034899496703 0.034899496703
0.052335956243 0.052335956243
0.069756473744 0.069756473744
0.087155742748 0.087155742748
0.104528463268 0.104528463268
0.121869343405 0.121869343405
0.139173100960 0.139173100960
0.156434465040 0.156434465040
0.173648177667 0.173648177667
0.190808995377 0.190808995377
0.207911690818 0.207911690818
0.224951054344 0.224951054344
0.241921895600 0.241921895600
0.258819045103 0.258819045103
0.275637355817 0.275637355817
0.292371704723 0.292371704723
0.309016994375 0.309016994375
0.325568154457 0.325568154457

Regards,
Dan

--
Dan Sommers
<http://www.tombstoneze ro.net/dan/>
Never play leapfrog with a unicorn.

[Frank Millman]

Frank Millman wrote:

Hi all

I was helping my niece with her trigonometry homework last night. Her
calculator's batteries were flat, so I thought I would use Python's
math module to calculate sin, cos, and tan.
Can someone please explain these discrepancies?

Thank you so much for the explanations, everyone. I appreciate your
patience.

I agree with Timothy's suggestion about adding a note to the
documentation. Obviously the math module is designed for those that
know what they are doing. However, you will always get the odd guy
like me that has some vague recollection of trigonometry from school
days, but does not really understand it, so it should help to avoid
similar confusion in the future.

Frank

[Roel Schroeven]

Dan Sommers wrote:

On 23 Jul 2004 23:00:18 -0700,
da*****@yahoo.c om (Dan Bishop) wrote:

def mysin(x):
return math.sin(math.r adians(x % 360))

Why?

for x in range( 20 ):
print '%.12f %.12f' % (math.sin( math.radians( x ) ), math.sin( math.radians( x % 360 ) ))

0.000000000000 0.000000000000
0.017452406437 0.017452406437
0.034899496703 0.034899496703
0.052335956243 0.052335956243
0.069756473744 0.069756473744
0.087155742748 0.087155742748
0.104528463268 0.104528463268
0.121869343405 0.121869343405
0.139173100960 0.139173100960
0.156434465040 0.156434465040
0.173648177667 0.173648177667
0.190808995377 0.190808995377
0.207911690818 0.207911690818
0.224951054344 0.224951054344
0.241921895600 0.241921895600
0.258819045103 0.258819045103
0.275637355817 0.275637355817
0.292371704723 0.292371704723
0.309016994375 0.309016994375
0.325568154457 0.325568154457

for x in range(10000000, 10000020): print '%.12f %.12f' %

(math.sin( math.radians( x ) ), math.sin( math.radians( x % 360 ) ))

-0.984807753010 -0.984807753012
-0.981627183449 -0.981627183448
-0.978147600733 -0.978147600734
-0.974370064789 -0.974370064785
-0.970295726278 -0.970295726276
-0.965925826288 -0.965925826289
-0.961261695942 -0.961261695938
-0.956304755964 -0.956304755963
-0.951056516293 -0.951056516295
-0.945518575604 -0.945518575599
-0.939692620787 -0.939692620786
-0.933580426495 -0.933580426497
-0.927183854571 -0.927183854567
-0.920504853453 -0.920504853452
-0.913545457639 -0.913545457643
-0.906307787041 -0.906307787037
-0.898794046299 -0.898794046299
-0.891006524183 -0.891006524188
-0.882947592863 -0.882947592859
-0.874619707138 -0.874619707139

When the numbers get larger, floats start losing precision. If you
restrict the numbers to the range [0, 360[ before conversion to radians
(and hence to degrees), that problem doesn't exist.

--
"Codito ergo sum"
Roel Schroeven

[Peter Otten]

Roel Schroeven wrote:

When the numbers get larger, floats start losing precision. If you
restrict the numbers to the range [0, 360[ before conversion to radians
(and hence to degrees), that problem doesn't exist.

(360**100 +0.0) % 360

184.0

Rule of thumb: floats are always inaccurate. % may only help when you are
dealing with large integers denoting an angle in degrees - an unlikely
scenario methinks.

Peter

[Roel Schroeven]

Peter Otten wrote:

Roel Schroeven wrote:

When the numbers get larger, floats start losing precision. If you
restrict the numbers to the range [0, 360[ before conversion to radians
(and hence to degrees), that problem doesn't exist.

(360**100 +0.0) % 360

184.0

Rule of thumb: floats are always inaccurate. % may only help when you are
dealing with large integers denoting an angle in degrees - an unlikely
scenario methinks.

Ok, you're right, I only considered the case where the input is
specified in degrees.

Anyway, when dealing with angles it's in most cases very well possible
to keep the values small by doing % 360 or % (2*pi) in all relevant
operations on the angles.

--
"Codito ergo sum"
Roel Schroeven

[Dan Bishop]

Dan Sommers <[e-mail] > wrote in message news:<m2******* *****@unique.fu lly.qualified.d omain.name.yeah .right>...

On 23 Jul 2004 23:00:18 -0700,
da*****@yahoo.c om (Dan Bishop) wrote:

da*****@yahoo.c om (Dan Bishop) wrote in message news:<ad******* *************** ****@posting.go ogle.com>...

def mysin(x):
return math.sin(math.r adians(x))

Even better:

def mysin(x):
return math.sin(math.r adians(x % 360))

Why?
for x in range( 20 ): print '%.12f %.12f' % (math.sin( math.radians( x ) ), math.sin( math.radians( x % 360 ) ))
[2 identical columns]

It's not suprising that they're identical: When 0 <= x < 360, then x % 360 == x.

However,

x = 360000000000L # a billion revolutions
math.sin(math.r adians(x)) -6.6394736764063 769e-08 math.sin(math.r adians(x % 360))

0.0

[Dan Sommers]

On 24 Jul 2004 12:44:30 -0700,
da*****@yahoo.c om (Dan Bishop) wrote:

Dan Sommers <[e-mail] > wrote in message news:<m2******* *****@unique.fu lly.qualified.d omain.name.yeah .right>...

On 23 Jul 2004 23:00:18 -0700,
da*****@yahoo.c om (Dan Bishop) wrote:

> da*****@yahoo.c om (Dan Bishop) wrote in message news:<ad******* *************** ****@posting.go ogle.com>...

>> def mysin(x):
>> return math.sin(math.r adians(x))

> Even better:

> def mysin(x):
> return math.sin(math.r adians(x % 360))

Why?

>>> for x in range( 20 ):

print '%.12f %.12f' % (math.sin( math.radians( x ) ), math.sin( math.radians( x % 360 ) ))
[2 identical columns]

It's not suprising that they're identical: When 0 <= x < 360, then x % 360 == x.

Yes, obviously, no surprise there. Duh! (smacks self on forehead)

I do, hoever, agree with Peter Otten about very large integers denoting
angles in degreen being unlikely. Usually, the 'mod 2pi' ends up in the
calculation of the angle rather than in the call to math.<whatever> .

Regards,
Dan

--
Dan Sommers
<http://www.tombstoneze ro.net/dan/>
Never play leapfrog with a unicorn.