# Definition of Sin or Cos

• Apr 9th 2005, 02:22 PM
Math Dude
Definition of Sin or Cos
Where do sin and cos come from.

I use them on my caluclator but I never really understand where they are getting the number from. My teacher keeps mentioning that when he was a student a hundred years ago they had to look up all of the values in a book.

so where do the values come from. could I derive them myself?
• Apr 9th 2005, 04:51 PM
paultwang
See MathWorld - Sine and MathWorld - Cosine.

One can express Sine and Cosine in natural exponents or infinite series.
• Apr 10th 2005, 03:00 AM
theprof
Quote:

Originally Posted by Math Dude
Where do sin and cos come from.

I use them on my caluclator but I never really understand where they are getting the number from. My teacher keeps mentioning that when he was a student a hundred years ago they had to look up all of the values in a book.

so where do the values come from. could I derive them myself?

For sure!
There are formulas that do the work very well, but are quite difficult to explain expecially if you have not studied calculus.
The name is Taylor's formula
http://www.math.jhu.edu/courses/107/...es/node34.html

But here is an example
you get something like
0.09983341664

Now try with this:
x - x^3/6
if you put 0.1 = 1/10 in place of x you get
1/10 -1/6000 ~ 0.09983333333
how many decimal digit are correct? Six!

Better results (and longer calculation) are obtained if you use
x^5/120 - x^3/6 + x
0.1^5/120 - 0.1^3/6 + 0.1 ~ 0.09983341666
Ten decimal digits are correct!
They are long calculation to be made by hand, aren't they?

Once matematicians made all by hand. Look at you calculator with more respect from now on ;)

bye