SIN/ASIN Question

  • Thread starter Thread starter Steve Almond
  • Start date Start date
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Steve Almond

If I find the sine of, say, 9 I get the following:

SIN(9) = 0.412118

if I take the ASIN of this answer:

ASIN(0.412118) = 0.424778

Why do I not get the answer = 9 ?

Thanks,

Steve
 
sin(x+2*PI()*n) = sin(x)

for any integer n. Since there are infinitely many numbers that would
produce a given sine, asin only makes sense in the context of a
convention for which of infinitely many values it will return. As
documented in Help, asin returns the particular inverse value that is
between -pi/2 and pi/2

Jerry
 
Jerry,

Thanks for the reply. As I'm struggling with this I'll relate the context.
I was looking at a webpage which was "testing" the accuracy of some
calculators.
to do this they calculated the following for each:

asin(acos(atan(tan(cos((sin(9)))))) =?

with the calculator in degrees mode.

They got answers ranging from 6.58(!) to 71.2(!!) most, of course, right
around 9.000.
I thought I would replicate the test in Excel, but I'm unsure how to account
for "in degrees mode".
I can calculate

=DEGREES(ASIN(ACOS(ATAN(TAN(COS(SIN(RADIANS(9))))))))

and get

9.0000000000000100

maybe that's as far as it goes?


Here's the calculator page
http://forensics.calcinfo.com/

Steve
 
Excel does not have a "degrees mode"
=DEGREES(ASIN(SIN(RADIANS(9))))
returns 9

More generally nest a RADIANS() function inside each trig function and
nest each inverse trig function inside a DEGREES function. You will
have to split this over multiple cells since Excel only supports 7
levels of nesting.

Jerry
 
Excel does not have a "degrees mode"
Click to expand...
...

DIGRESSION!

I'm currious what everyone would think about an option to switch between degrees
and radians for trig functions. That is, there's a user option to choose 1904
date system rather than 1900 date system. It's possible (though it's not current
functionality) that a similar setting could be added for trig functions to
assume arguments in degrees rather than radians. Given that switching date
systems causes some problems, this could be viewed as creating even more
problems. Then again, as this thread illustrates, using radians isn't second
nature to many (most?) Excel users.

Seriously, what does everyone think about this?
 
Harlan said:
...
..

DIGRESSION!

I'm currious what everyone would think about an option to switch
between degrees and radians for trig functions. That is, there's a
user option to choose 1904 date system rather than 1900 date system.
It's possible (though it's not current functionality) that a similar
setting could be added for trig functions to assume arguments in
degrees rather than radians. Given that switching date systems causes
some problems, this could be viewed as creating even more problems.
Then again, as this thread illustrates, using radians isn't second
nature to many (most?) Excel users.

Seriously, what does everyone think about this?
Click to expand...

Hi Harlan

Hopefully there will never be a switch for this. I agree with you that
this would definetly create additional problems sharing workbooks,
pasting formulas, etc.

Not sure about the other users but during my school/university time the
usage of radians was quite common (you only have to agree on a common
definition whether to use degrees or radians before).
 
Hi Harlan!

Sounds like a good idea. Only drawback I can see is that users would
have to be awake to the fact that the option can be changed and that
this will affect the results of all formulas that used the other
setting.

But perhaps Status Bar warnings "Degrees Mode" and "1904 Date System"
might help.

--
Regards
Norman Harker MVP (Excel)
Sydney, Australia
(e-mail address removed)
Excel and Word Function Lists (Classifications, Syntax and Arguments)
available free to good homes.
 
Harlan Grove said:
Seriously, what does everyone think about this?
Click to expand...

My immediate impression is that it would cause a tremendous decrease in
the reliability of models. Dates can cause *some* grief, though for most
users it's transparent. But it's also *usually* obvious when a date is
FUBARed - 4 years and a day is an easily recognizable deviation from an
expected value.

With trig functions, however, I suspect that non-engineers/geometers
(and a fair number of engineers as well) would on balance have an
extremely hard time recognizing an incorrect result. How many would
recognize this difference at a glance?

=SIN(40) ===> 0.74511316 (radians mode)
=SIN(40) ===> 0.64278761 (degrees mode)

I agree with the spirit of your suggestion, though. I think I'd rather
see (without any real understanding of the difficulty of implementation)
an optional argument added to trig functions to trigger conversion:

=SIN(90) = SIN(90, 1) ===> 0.893996664

and

=SIN(90, 2) ===> 1.000000000

The downside is that this would break backward compatibility. A more
bloated option would be to add functions (which I've done via add-ins
before):

SIN(90) ===> 0.893996664
SIND(90) ===> 1.000000000
 
Rather than a mode, why not an optional argument (defaulting to radians)
to specify how angles are measured. That way there would be no
compatibility issues.

Jerry
 
Jerry W. Lewis said:
Rather than a mode, why not an optional argument (defaulting to
radians) to specify how angles are measured. That way there would
be no compatibility issues.
Click to expand...
....

That'd be one way, but that leaves the issue of new users not knowing about
the optional argument. Also makes it a pain to have to use the optional
argument all the time if you want optional functionality.
 
Having worked in a machine for more years than I care to remember, I've
always used degrees, never radians. Having used an old DOS spreadsheet (with
limited capabilities), my formulas were always written to convert radians to
degrees to arrive at the proper answer. (spreadsheet did not have the
"RADIANS"--"DEGREES" functions)

Walter Mayes
 
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