What is the real algebra going on behind the sin and cosin functions. When I say 'real' I mean the very basic math. Is there a plain formula that is being done say for instance when you hit sin on a calculator?

http://www.gcseguide.co.uk/sin,_cos,_tan.htm

http://www.google.com/search?q=sin+cos

If you have a right triangle, then:

sine of the angle = length of the opposite side / length of the hypotenuse

cosine of the angle = length of the adjacent side / length of the hypotenuse

tangent of the angle = length of the opposite side / length of the adjacent side

http://www.google.com/search?q=sin+cos

If you have a right triangle, then:

sine of the angle = length of the opposite side / length of the hypotenuse

cosine of the angle = length of the adjacent side / length of the hypotenuse

tangent of the angle = length of the opposite side / length of the adjacent side

hiii

there isnt any exac formula for calculate trigo function (sin,cos and tan) .. you can do tricks and calculate the angles i can calculate sin(18) with out any calculate but you cant calculate everything .. i heard that they calculated sin(1) without calculator .

mathmatition has turned those functions to sequences i knew sin functions . but i cant remember it right now . when i find it i'll post

bye

eko

there isnt any exac formula for calculate trigo function (sin,cos and tan) .. you can do tricks and calculate the angles i can calculate sin(18) with out any calculate but you cant calculate everything .. i heard that they calculated sin(1) without calculator .

mathmatition has turned those functions to sequences i knew sin functions . but i cant remember it right now . when i find it i'll post

bye

eko

Here are the formulas you need (copied from my math book :grin: )

Thanks LuHa, that made clear to me why many programs use sin/cos tables :grin:

You know what I'm wondering about? how do people find that out? i mean this sine stuff that LuHa posted...... can someone explain that to me? you know, i'm someone who wants to know why, and not only how...

nop

nop

Hi NOP !

The Taylor-Formular given by LuHa descripes an approximation of the function f(x) at a value near x

If you take the first two terms of this sum you get a linear approximation: you start at the point (x, f(x)) and draw a line which is the tangential line of f at (x,f(x)), which gradient is just f'(x) !

In very low distance from x this linear approximation is near the real value of f(x) but if you increase this distance this proximity gets worst.

To get better approximations you need to add non-linear terms and those are the higher order derivatives.

To get a good approximation of Sin(x) starting from x=0 up to x=Pi/4 then you need at least the first 7 .. 9 terms of this Taylor-Sum. Setting X = 0 the values f(0), f'(0), ... f''''''''(0) will be 0, -1 or +1. This is the sum LuHa wrote for Sin(x).

Greetings, CALEB

The Taylor-Formular given by LuHa descripes an approximation of the function f(x) at a value near x

If you take the first two terms of this sum you get a linear approximation: you start at the point (x, f(x)) and draw a line which is the tangential line of f at (x,f(x)), which gradient is just f'(x) !

In very low distance from x this linear approximation is near the real value of f(x) but if you increase this distance this proximity gets worst.

To get better approximations you need to add non-linear terms and those are the higher order derivatives.

To get a good approximation of Sin(x) starting from x=0 up to x=Pi/4 then you need at least the first 7 .. 9 terms of this Taylor-Sum. Setting X = 0 the values f(0), f'(0), ... f''''''''(0) will be 0, -1 or +1. This is the sum LuHa wrote for Sin(x).

Greetings, CALEB

hey caleb,

thanks for that explanation!

NOP

thanks for that explanation!

NOP