Jump to content

Finding the Sine, Cosine, and Tangent without a caculator


Lightmeow

Recommended Posts

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

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

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

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 by Lightmeow
Link to comment
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.