Lightmeow Posted December 1, 2013 Share Posted December 1, 2013 I did a google search of this, and didn't get far... How would you find the sine of, say pi/2 radians.(Of course, this is 1, just wanted to keep things simple). I'm sure that some caculators have an algorithm to find the sine of a number, and how did people find it out back when they didn't have caculators. Just curious... And I am just talking about finding the sine, and the others with just one number, the number you are finding the ratio with. Say I wouldn't give you any other information, no other angles or lengths. Thank's for your time Link to comment Share on other sites More sharing options...

Janus Posted December 1, 2013 Share Posted December 1, 2013 (edited) You can use the Taylor series: [math]\sin x = x- \frac{x^3}{3!}+ \frac{x^5}{5!}- \frac{x^7}{7!}...[/math] Edited December 2, 2013 by Janus Link to comment Share on other sites More sharing options...

Lightmeow Posted December 1, 2013 Author Share Posted December 1, 2013 You can use the Taylor series: [math]\sin x = \frac{x^3}{3!}+ \frac{x^5}{5!}+ \frac{x^7}{7!}...[/math] I would assume that with the Taylor series, you cannot use degrees, because that would screw everything up. Edit, of course it would, don't even reply to that, I am so stupid Link to comment Share on other sites More sharing options...

mathematic Posted December 1, 2013 Share Posted December 1, 2013 You can use the Taylor series: [math]\sin x = \frac{x^3}{3!}+ \frac{x^5}{5!}+ \frac{x^7}{7!}...[/math] Your series is wrong. The first term is x and the terms alternate in sign. Link to comment Share on other sites More sharing options...

Bignose Posted December 2, 2013 Share Posted December 2, 2013 and 'without a calculator' is actually a fairly broad condition. Because would that allow me to use a slide rule? How about a wheel with the trig funtions on it (like http://thumbs1.ebaystatic.com/d/l225/m/mY0p2yLqWcm_BM6fIlsKGXQ.jpg)? Or what more people did before speedy calculation was available... look it up in a table (like http://upload.wikimedia.org/wikipedia/commons/2/2e/Abramowitz%26Stegun.page97.agr.jpg). Also, might want to have a read through this recent thread on a very similar topic: http://www.scienceforums.net/topic/78655-how-do-you-get-the-sine-of-an-angle-without-calculator/ Link to comment Share on other sites More sharing options...

Janus Posted December 2, 2013 Share Posted December 2, 2013 Your series is wrong. The first term is x and the terms alternate in sign. Oops! I was paying so much attention to the LaTex for the fractions, that I missed that. Thanks. I have gone back and corrected it. Link to comment Share on other sites More sharing options...

Lightmeow Posted December 2, 2013 Author Share Posted December 2, 2013 (edited) and 'without a calculator' is actually a fairly broad condition. Because would that allow me to use a slide rule? How about a wheel with the trig funtions on it (like http://thumbs1.ebaystatic.com/d/l225/m/mY0p2yLqWcm_BM6fIlsKGXQ.jpg)? Or what more people did before speedy calculation was available... look it up in a table (like http://upload.wikimedia.org/wikipedia/commons/2/2e/Abramowitz%26Stegun.page97.agr.jpg). Also, might want to have a read through this recent thread on a very similar topic: http://www.scienceforums.net/topic/78655-how-do-you-get-the-sine-of-an-angle-without-calculator/ I was referring to the way you were to do it, if there was a formula or the such. Yes you could use a slide rule, and yes you could use a calculator. A am aware that people had a table(my dad was a surveyor and he has a book, called the book of sines). I was simply asking for a way to find it without pressing the sine button on a calculator, or making an approximation via table.(Which I know some calculators have a table programmed in and do estimate) I also read the thread, sorry for not looking there before I posted it, because that would of answered my question. Edited December 2, 2013 by Lightmeow Link to comment Share on other sites More sharing options...

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