Finding the Sine, Cosine, and Tangent without a caculator

[Lightmeow]

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

[Janus]

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

[Lightmeow]

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

[mathematic]

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.

[Bignose]

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/

[Janus]

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.

[Lightmeow]

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