Sine of the times.
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06-12-2024, 07:32 PM
Post: #1
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Sine of the times.
Hi all.
Just befuddled. How did sin(x)² (cosh(x)², csc(x)², etc.) come to be interpreted as sin² x or (sin x)², etc.? To me sin(x)² represents x x² SIN. But, clearly, I must have missed the memo. |
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06-12-2024, 08:54 PM
Post: #2
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RE: Sine of the times.
Because computers and calculators have polluted your thinking. You are using the computer function notation. In math texts there are no parens. Attached is a page from Big Red showing the entry for sin.
Note that it is just sin z. So putting sin^2 z removes any ambiguity between sin z^2 or (sin z)^2. |
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06-12-2024, 08:56 PM
Post: #3
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RE: Sine of the times.
(06-12-2024 07:32 PM)Matt Agajanian Wrote: Just befuddled. How did sin(x)² (cosh(x)², csc(x)², etc.) come to be interpreted as sin² x or (sin x)², etc.? To me sin(x)² represents x x² SIN. But, clearly, I must have missed the memo. When I first saw this back in middle or high school it confused me too. I thought sin²x might stand for sin(sin(x)) as in function composition. After all, x² = xx hence f²x=ffx so why not? It's my comp sci slash physics brain I suppose. - Rob "I count on old friends to remain rational" |
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06-12-2024, 08:58 PM
(This post was last modified: 06-12-2024 09:01 PM by Nigel (UK).)
Post: #4
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RE: Sine of the times.
(06-12-2024 07:32 PM)Matt Agajanian Wrote: Hi all. The problem with \(\sin(x)^2\) is that it is ambiguous - is it just \(x\) that's being squared, or is it \(\sin(x)\)? Writing \(\sin^2x\) makes the intent plain without the need for (extra) brackets. Since squared trig functions are so common, it's a very popular time-saving notation. You did indeed miss the memo. I've found a reference (scroll down the page to find it) to Laplace having used this notation; Gauss found this odious, because he felt that \(\sin^2(x)\) should mean \(\sin(\sin(x))\) (and he has a point!) but since the repeated sine is used so rarely this isn't an issue in practice. Nigel (UK) (Added) Just to confuse things, \(\sin^{-1}x\) means the inverse sine of \(x\), not \(1/\sin(x)\)! |
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06-12-2024, 10:51 PM
(This post was last modified: 06-13-2024 02:48 AM by Matt Agajanian.)
Post: #5
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RE: Sine of the times.
(06-12-2024 08:58 PM)Nigel (UK) Wrote:(06-12-2024 07:32 PM)Matt Agajanian Wrote: Hi all. You see my point exactly! At 58, an avid calculator user and collector since six years of age, I've grown up with sin⁻⁻¹(x) & sin⁻¹ x notation. So, that's first nature to me. What I've read from a Reddit response to post I've made of this same question, I was told that since EOS, WriteView, and DAL do not allow the entry of sin² notation and immediately enter sin(, you cannot rewrite it as sin² but sin(x)² is the available option and entry method, kids nowadays have been indoctrinated that sin(x)² is now the written and textbook standard (!blasphemy! in my book). |
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06-13-2024, 08:24 AM
(This post was last modified: 06-13-2024 11:49 AM by carey.)
Post: #6
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RE: Sine of the times.
(06-12-2024 10:51 PM)Matt Agajanian Wrote: What I've read from a Reddit response to post I've made of this same question, I was told that since EOS, WriteView, and DAL do not allow the entry of sin² notation and immediately enter sin(, you cannot rewrite it as sin² but sin(x)² is the available option and entry method, kids nowadays have been indoctrinated that sin(x)² is now the written and textbook standard (!blasphemy! in my book). The HP 17bii avoided this issue by not including any trigonometric functions! :) |
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06-13-2024, 05:27 PM
Post: #7
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RE: Sine of the times.
I like sin(x)^2 notation. Say out loud, it is the same order: sine x squared.
Inverse Trig Notation: What Do sin^-1 and arcsin Mean? Quote:you find that early forms of "arcsin" arose in the 1700s, and the sin^2 notation came at the same time; This may explain why sin^2(x) cannot mean sin(sin(x)), I wish it did. Notation were already taken long time ago. |
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06-13-2024, 05:59 PM
Post: #8
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RE: Sine of the times.
(06-13-2024 05:27 PM)Albert Chan Wrote: I like sin(x)^2 notation. Say out loud, it is the same order: sine x squared. Although, the statement itself, without punctuation as you have it can mean two things: Sine of x squared: (sin(x))² Sine of x squared: sin(x²) But Sine of the square of x describes the order: first take the square of x. Then take the sine of that value, Whereas The square of the sine of x means to take the sine of x then square that value. |
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06-13-2024, 06:37 PM
Post: #9
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RE: Sine of the times.
Ah, punctuation! Thanks!
sin(x)^2 == sine x, squared sin(x^2) == sin of squared x |
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06-13-2024, 06:45 PM
(This post was last modified: 06-13-2024 06:46 PM by Matt Agajanian.)
Post: #10
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RE: Sine of the times.
Just a note. My above comment wasn’t meant for some show of intellectual superiority. I’m simply pointing out that even the English language needs some means to ensure clarity and precision of meaning.
Full apologies to anyone offended by my grammar/language police efforts. |
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06-14-2024, 10:34 AM
Post: #11
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RE: Sine of the times. | |||
06-14-2024, 10:48 AM
Post: #12
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RE: Sine of the times.
Hello,
(06-14-2024 10:34 AM)WillMarchant Wrote: Please pardon my ignorance, but what’s “Big Red”? From the contents it must be this book (the clipping above is on page 71): https://personal.math.ubc.ca/~cbm/aands/...stegun.pdf Although mine is blue and the one in the link is not red either. Regards Max |
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06-14-2024, 01:58 PM
Post: #13
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RE: Sine of the times.
Wow, I thought this was a common nickname. That is what my professor in college called it.
Yes, Abramowitz and Stegun, Handbook of Mathematical functions. In the early eighties, I went down to the Government printing office store at a mall in downtown LA to pick up a copy. You used to be able to buy Topo maps there, too. |
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06-15-2024, 01:10 AM
Post: #14
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RE: Sine of the times.
(06-14-2024 10:48 AM)Maximilian Hohmann Wrote: Hello, WOWZA! Thanks! Now I’ve got a copy of this landmark encyclopedia!! |
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06-15-2024, 01:18 AM
Post: #15
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RE: Sine of the times.
(06-15-2024 01:10 AM)Matt Agajanian Wrote:(06-14-2024 10:48 AM)Maximilian Hohmann Wrote: Hello, Printed copies of this historically and technically amazing book are surprisingly common and readily and cheaply available; for example, on ABE there's a copy there now for $10.00 with free shipping. --Bob Prosperi |
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06-18-2024, 07:49 PM
Post: #16
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RE: Sine of the times.
(06-12-2024 08:58 PM)Nigel (UK) Wrote: Gauss found this odious, because he felt that \(\sin^2(x)\) should mean \(\sin(\sin(x))\) (and he has a point!) but since the repeated sine is used so rarely this isn't an issue in practice. Mathematician Kenneth Iverson also balked at these inconsistencies in math notation, and sought to fix it once and for all. APL was the result. "Be careful what you wish for: you may get it..." Daily drivers: 15c, 32sII, 35s, 41cx, 48g, WP 34s/31s. Favorite: 16c. Latest: 15ce, 48s, 50g. Gateway drug: 28s found in yard sale ~2009. |
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06-18-2024, 11:55 PM
Post: #17
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RE: Sine of the times.
(06-18-2024 07:49 PM)johnb Wrote: Mathematician Kenneth Iverson also balked at these inconsistencies in math notation, and sought to fix it once and for all. For anyone interested in array languages, of which APL is the most notable example, there's a podcast on array languages "The Array Cast". A recent episode was an interview with the developer of a free APL system (NARS2000) that includes a toolbar of APL glyphs (no APL keyboard needed), so you can decide if APL was a bad idea, a good idea, or just fun. |
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06-19-2024, 12:04 AM
Post: #18
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RE: Sine of the times.
(06-15-2024 01:18 AM)rprosperi Wrote: Printed copies of this historically and technically amazing book are surprisingly common and readily and cheaply available; for example, on ABE there's a copy there now for $10.00 with free shipping. Yup, Abramowitz and Stegun was the bible for many years in school. I've never heard it called the "Big Red" either. Everyone around me had the Dover edition which is a big blue book. I have the 9th Dover printing, which claims to be same as the 10th printing (December 1972) of the original, with some additional corrections. As far as I can tell from Amazon, the 9th Dover printing is still the most recent. The cheapest used price at Amazon is $7.91, incl shipping. |
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06-19-2024, 05:35 AM
Post: #19
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RE: Sine of the times.
Mine was actually printed by the US Gov printing office.
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06-19-2024, 06:36 AM
Post: #20
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RE: Sine of the times.
The current seminal work, not least for notational questions seems to be
https://dlmf.nist.gov NIST Handbook of Mathematical Functions This is intended to superseed Abramowitz, Stegun. The tables are gone, but the equations at still there, lots of them. The webpage is updated constantly. The printed version is a big red book. Felix |
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