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A question to non-Russians. I've read some article. I don't believe it, but... it really awoke my interest. Strong interest. I know that my doubt may offend you, but I can't suffer any more. Execuse me, if you find my question insulting.
OK, here's the most stupid question I've ever asked:
Do you know why sin30 = 0,5?
Um...this is a mathematical operation.
The sine (abbreviated "sin") of an angle measurement of 30 degrees is equal to 0.5
sin(30)=0.5
This is the only way I can make sense of that....
LOL...how did you come about this?
sin(30) = 0.5
The sine of a 30 degree angle is 0.5.
That means if you shoot something at a 30 degree angle, the height attained is half of the distance covered. (But that is assuming there is no gravity.) :D
http://www.gcse.com/maths/images/sin30.gif
Because, my friend, when a triangle has the angle of 30 degrees, the hypotenus is double as long as the opposite! ALWAYS! And then the ratio will always be 1/2!
sin X = Opposite / Hypotenus
PS: Opposite is the line which is opposite the angle X and hypotenus is that really long line opposite the 90 deg
I am impressed with your math skills!
Well, it is kind of my job to know math... :P
Anyway, how do you spell sinus / sine / sin in Russian? Do you use latin letters or what?
синус
Ha! That was on my Algebra final this year! SohCahToa! I think, I can't remember. I wrote it on my hand. :roll:
SohCahToa is what got me through those courses...I can never forget it.
I miss my Algebra class! I had so much fun there! :lol: Even if I can't really remember much. -Wipes tear-
Edit:
Why am I capitalizing Algebra?
Вопрос, видимо, навеян этой статьёй :lol:
http://nauka.relis.ru/05/0412/05412020.htm
OK, kalinka, what must I do when X > 180? sin270 = -1, but can you give me a triangle with 270 degrees angle? :wink:Quote:
sin X = Opposite / Hypotenus
You're right!Quote:
Originally Posted by N
But just understand, I don't want to offend somebody. The article describes such fantastic things, unbelievable things! So unbelievable for me, that my interest doesn't allow me to be calm!
Sorry Pranky but when they started to mix numbers with the alphabet they lost me.
Well, ok, this method it only works for < 90 degreesQuote:
Originally Posted by pranki
For larger values... you have to learn... the... dreaded... UNIT CIRCLE (dramatic music)
http://www2.spsu.edu/math/edwards/1113/unit2.gif
Hint: - If you are doing a sine of the angle, look for the intersection from the unit circle's circumfrance to the vertical line (for cosinus to the horizontal line)
kalinka, you're quite right!!! Now I know, that the article lies!
But let's think about the following. How does your calculator get values of sine? Does it draw the unit circle (thanks for the term, I didn't know how does единичная окружность sound in English) in its memory, look for intersections etc?
What's so unbelievable about it? *Shrug*Quote:
Originally Posted by pranki
pranki, do _you_ really know how exactly it gets the values? i suspect it might well depend on the calculator (unless there is one cheap chinese chip that everyone uses)Quote:
Originally Posted by pranki
I just wanted to get the most common definition of sine.Quote:
Originally Posted by laxxy
OK, I call off my last question. It isn't fairly, because it is learned in univesity departments, which are dedicated to mathematics, and ordinary people don't have to know this.
I'm sorry.
Aah!!! Get this crap out of my face! I had to take 22 semesters of Advanced Algebra / Advanced Calc in school! I've spent years erasing this all from my memory! :lol:
-Fantom
ps- TriggerHappyJack, I have the habit of capitalizing Algebra and Calc also, maybe it's our nature to capitalize things that suck a lot...!
i think the most common definition is the one with the unit circle (maybe with the triangle at school at first), just as in russia...Quote:
Originally Posted by pranki
i suspect the calculators use some combination of lookup tables and series expansion, but i can not be sure...
Sine is defined as the ratio of the opposite side to the hypotenuse of a right-angled triangle .
A calculator does not find a sine value by reading it off a list. Instead, it uses an algorithm to find an approximate value.
One algorithm is the Taylor algorithm, which is:
sin x = x - x^3/3! + x^5/5! - x^7/7! + x^9/9!...
and so on, following that pattern. The farther you go out, the more accurate the result.
Another method is using the CORDIC algorithm which stands for Coordinate Rotation Digital Computer. This method is a bit complicated, so basically all you need to know is that it "rotates" the phase of a complex number, by multiplying it by a constant values.
For more information on CORDIC algorithm, look here:
http://www.dspguru.com/info/faqs/cordic.htm
The most common definition uses Taylor series.Quote:
i think the most common definition is the one with the unit circle (maybe with the triangle at school at first)
I would suspect that most "simple" calculators would use the taylor series. The more advanced calculators and computers, which are capable of graphing, may use a combination of both Taylor and CORDIC.
I read a little of the article (quite a long one!), it basically is saying that we as the human race (with france and the "west" as an example) are getting stupider by the generation, because we have all these devices that does the thinking for us (and Russia as the exception). Students don't worry about how to calculate sin(35.234234), because the calculater does it for us.
I somewhat disagree. I agree that people are becoming more dependent on computers to do the basic mathematics (like adding and subtraction), but we also use it for the advanced mathematics which is almost impossible (or at least very time consuming) to calculate without a computer. Not many people in the previous generations could find the answer to sin(35.234234) in 5 seconds.
We might not know what tan(25) is off the top of our heads, unless we are certain mathematicians or other proffesions that involve trigometry. But, our previous generations didn't have to worry about doing complicated tasks as programming computers, operating machinery, distill overwhelming amounts of information, etc. Besides, if you compare to the percentage of people who take a degree or even literacy precentage with 50 years ago, we have vastly improved the quantity and quality of human knowledge!
kalinka, I think the main idea of the article is here:
I think, there is much true in it, and in Russia we have the same process. Yesterday's news from the Russian Ministry of Education:Quote:
Этот крайне циничный взгляд на современное общество как-то растолковал мне один мой коллега по университету (огромный патриот Франции, по происхождению поляк, несколько лет проучившийся в Москве, прекрасно говорящий по-русски, большой знаток русской литературы). Он очень умный человек, тоже преподает и прекрасно видит, что происходит, но при этом считает, что никакой катастрофы нет, а наоборот, все правильно, все развивается как надо. Дело в том, что современному развитому обществу нужны только хорошие исполнители. Творческие, думающие люди, конечно, тоже требуются, но буквально единицы. Поэтому вся система образования должна быть настроена на отбор, выращивание и дрессировку именно хороших исполнителей, а учить думать молодых людей совершенно не нужно: в современном обществе это только повредит их будущей профессиональной деятельности, какой бы она ни была. Что же касается творческих личностей, то о них особенно беспокоиться не следует: тот, кто действительно талантлив, так или иначе все равно пробьется. В этом смысле, по большому счету, совершенно не важно, каким предметам мы их тут, в университете, учим (по крайней мере на первых курсах). Вместо физики с математикой вполне можно было бы заставлять зубрить, например, латынь (вот только специалистов таких сейчас не сыщешь). Все равно в будущей профессиональной деятельности никакое понимание физики с математикой им не понадобится. На уровне школы и университета важно просто производить отбор и дрессировку самых послушных, трудолюбивых и исполнительных, вот и все. А для тех, кто вылетает из этой системы, для тех, кто идет в "отходы", существуют метлы для подметания улиц, кассовые аппараты в супермаркетах, заводские конвейеры и т. д. Вы вон в Советском Союзе в свое время напроизводили миллионы образованных "думающих" инженеров - и что? По части своих прямых профессиональных обязанностей они, как правило, ни черта делать не умели, а предпочитали размышлять о судьбах мира, о смысле жизни, о Достоевском... Причем, согласитесь, сами эти, так сказать, "думающие образованные инженеры" сплошь и рядом чувствовали себя несчастными людьми: невоплощенные мечты о великих свершениях, нереализованные таланты, мировая скорбь и тому подобное. А тут жизненные претензии и запросы, как личные, так и профессиональные, четко алгоритмированы, и все счастливы и довольны...
http://top.rbc.ru/index.shtml?/news/day ... _bod.shtml
They again and again raise the question about how old Soviet standards are hard for our children and they lost theirs health studying science.
Elite teachs theirs children in elite schools and they don't want competitors for them from low classes.
This is one of the few things in math i was good at.
Sine of angle= opposite side length divided by hypotenuse
Cosine of angle= adjacent side length divided by hypotenuse
Tan of angle= opposite side length divided by adjacent side length.
The easiest way to remember is
soh-cah-toa