There has been lurking in my mind a question for way too long, without being able to find a suitable, satisfying answer.

How are sin(), cos(), and tan() functions calculated on a calculator or computer?

I understand that mathematicians use the famous unit circle to define the trigonometric functions, but if

sin(ᴨ/4)=o/1

o= sin(ᴨ/4)*1

a=cos(ᴨ/4)*1

tan(ᴨ/4)=sin(ᴨ/4)

_______

cos(ᴨ/4)

So we are still left with the question, how is sine, cosine and tangent computed?

All the books and references that I read basically just suggest to use the calculator, in other words computed by magic or dogma.

Edit: I now remember that they use the Pythagorean theorem.

h²=o²+a²

ᶿ=ᴨ/4

o=a

1²=2o²

___

√1/2 = o

___

a= √1/2

___

sin(ᴨ/4)=√1/2

_____

1

___

cos(ᴨ/4)=√1/2

_____

1

___

tan(ᴨ/4)=√1/2

_____

√1/2

But how do they compute the rest of angles?

**Edited by gasto, 23 July 2014 - 11:39 AM.**