Invers sinus function

I beg to differ, Terry Moore. The sine function wasn't even known in Roman times - math wasn't that far along. I've studied both Latin and math, and there was no word for such a thing in Roman times.

English is one thing, but math is universal. It's the sine function if you know what you're doing in any language.

duffymoa at 2007-7-15 0:25:46 >

I've got an engineering background, and I never heard the general function referred to as a sinus function. The general category was trigonometric functions.

When I type "sinus function" into Google, it brings back a lot of medical articles about nose problems. There's a couple of forum notes, like the OP question, where people ask about sinus functions, but there isn't a single mathematical site that describes a unit amplitude sine function as a sinus.

Maybe it's a European thing.

I still say it's incorrect. At best, it's not a term in general usage. - MOD

duffymoa at 2007-7-15 0:25:46 >

Google tells me that you're correct about the Greeks having chords of circles, but the first appearance of the sine of an angle is credited to Hindus around 500 A.D.

Put down? No. Merely noting a fact. If you're looking for elliptic integrals, but don't know the name, you'll have a hard time finding those, too. - MOD

duffymoa at 2007-7-15 0:25:46 >

> Google tells me that you're correct about the Greeks

> having chords of circles, but the first appearance of

> the sine of an angle is credited to Hindus around 500

> A.D.

Yes, I've since looked up Britannica. Hipparchus, 2nd

century BC had 12 books of tables of chords--lost but

we have it on the authority of writers 500 years later

who called Hipparchus the father of trigonometry.

Ptolomy of Alexandria also had tables in 2nd century AD.

Remember that long after Latin ceased to be the

vernacular of the common people (if that's not a

tautology), it was the language of science until at

least the 18th century. When the Arabic books on

mathematics were translated into Latin in the 12th

century, the word for sine was mistranslated as sinus.

There's a lot more interesting stuff in the article

Trigonometry: history in Britannica.

> Put down? No. Merely noting a fact. If you're

> looking for elliptic integrals, but don't know the

> name, you'll have a hard time finding those, too. -

> MOD

OK.

TerryMoorea at 2007-7-15 0:25:46 >

> Yeah, but "asin"? That doesn't follow any mathematical

> usage I've ever seen, either. Why isn't it called

> "arcsin"?

There's a lot of inconsistency about, we just have to

get used to it. The inverse of a function is often

denoted by superscript -1. That's fine but not easy

to use in computer languages. Unfortunately, sin^2

ought, for consistency's sake, to be the sine of a

sine, but it's never used like that.

Then there's the horrible arcsinh seen in some languages

and texts.

The angle corresponding to a sine can be related to the

arc length of a circle, hence the name arcsine, but the

inverse hyperbolic sine is not an arc length but an area,

hence arsinh. asin and asinh are convenient abbreviations

where 'a' can be read as 'arc' or 'ar' as needed. I like

it. atan2 is also horrible, but a necessary evil in a

floating point world with the possibility of overflow.

TerryMoorea at 2007-7-15 0:25:46 >

> I disagree about one thing you wrote here, Terry.

> sin^2 makes me think "sine-squared" before "sine of

> sine". (I can't think of a time offhand when I've

> used sine of sine, but sine-squared is common for

> Fourier series.)

The usual meaning of "f squared of x" when you're talking about functions in general is "f(f(x))" and not "f(x) squared", but the trig functions are an exception to this.

DrClapa at 2007-7-19 5:46:27 >

> > I disagree about one thing you wrote here, Terry.

> > sin^2 makes me think "sine-squared" before "sine of

> > sine". (I can't think of a time offhand when I've

> > used sine of sine, but sine-squared is common for

> > Fourier series.)

>

> The usual meaning of "f squared of x" when you're

> talking about functions in general is "f(f(x))" and

> not "f(x) squared", but the trig functions are an

> exception to this.

Hm ... I guess things differ all over the globe; when I studied math, the usual notation was (I'm sprinkling in some parentheses for clarity)

sin^2(x) --> sin(sin(x))

sin(x^2) --> sin(x*x)

sin(x)^2 --> sin(x)*sin(x)

But then again a (hopefully small) section in the foreword, mentioning the notation used, does wonders most of the time.

kind regards,

Jos

JosHorsmeiera at 2007-7-19 5:46:27 >

> > sin^2(x) --> sin(sin(x))

> > sin(x^2) --> sin(x*x)

> > sin(x)^2 --> sin(x)*sin(x)

>

> hm, when i was at school

> sin^2(x) --> sin(x)*sin(x)

but

> f^2(x) --> f(f(x))

It's a matter of convenience. Powers of trig functions (more

precisely, powers of the result of applying trig functions)

occur so frequently that it's sensible to have a short notation

for it. sin^2 x = (sin(x))^2 is natural although inconsistent

with other uses of superscripts applied to functions.

I was just pointing out the inconsistency, not condemming it.

TerryMoorea at 2007-7-19 5:46:27 >