hello,
i've been thinking about this for a while now, and here it goes:
How does a calculator or any computer for that matter calculate trig functions
(lookup table; perhaps? and a linear approx in-between or Square function approx??)
My research lead to somehting called the Taylor series, but that gives an approximation.
Is there's a formula that can give a precise value like Sqrt(whatever)??
hello,
i've been thinking about this for a while now, and here it goes:
How does a calculator or any computer for that matter calculate trig functions
(lookup table; perhaps? and a linear approx in-between or Square function approx??)
My research lead to somehting called the Taylor series, but that gives an approximation.
Is there's a formula that can give a precise value like Sqrt(whatever)??
by precise i mean cos60 = 0.5 or cos 30 = sqrt(3)/2
pi is precise, but 3.14 is an approximation
cos x = +/- Sqrt(1 - (sin x)^2 ) is precise
is there a formula that gives me an expression of this form for any number, from which i can then find any approximation that i want
if so, please, enlighten me
Thanks
by precise i mean cos60 = 0.5 or cos 30 = sqrt(3)/2
pi is precise, but 3.14 is an approximation
cos x = +/- Sqrt(1 - (sin x)^2 ) is precise
is there a formula that gives me an expression of this form for any number, from which i can then find any approximation that i want
if so, please, enlighten me
Thanks
just wanted to point out that he got his equation from
(sin(x))^2 + (cos(x))^2 =1
Given the equation (sin(x))^2 + (cos(x))^2 = y, is there a most precise value that can be substituted for x that will result in y being equal to 0 because of precision?
Also, the examples that I gave about astronomy and subatomic particles in my last post may have been misleading.
The question may have been a lot more involved then I had at first thought. Out of curiosity, was it answered?
SIN(x)=x-x^3/6+x^5/120-x^7/5040+x^9/362880-x^11/39916800+x^13/6227020800-x^15/1307674368000+x^17/355687428096000-x^19/121645100408832000+x^21/51090942171709440000-x^23/25852016738884976640000+x^25/15511210043330985984000000-x^27/10888869450418352160768000000+x^29/8841761993739701954543616000000
The equation:
(sin(a))^2+(cos(a))^2=1
is not just some general equation, it is an identity.
Identities show a relationship between different things that happens to
be universal.
This particular one is a trigonometric identity, and results from looking
at an angle 'a' and the unit circle (radius=1). Thus,
sin(a) is the X coordinate, and cos(a) is the Y coordinate,
and X^2+Y^2=R^2=1.
This means that the '1' can never change to anything else.
It's also interesting that this relationship holds for complex numbers too.
I guess the geometrical interpretation then would be a surface 1 unit
up from the x,j*y plane.
No; i know what relative precision is, i wanted something of an abosolute precision (such as pie or sqrt(2))
i wanted a way to get the trigonometric lines of any angle in a nice clean formula such as: f(x)= x^2 but for cos or sin
(sin(a))^2+(cos(a))^2=1 is an identity. But is it different from (sin(a))^2+(cos(a))^2=y? My question - perhaps asked a little better in this post, is if the precision of a could be different from the precision of y when values for either one of these variables are substituted into the equation. I think that there are different ways of determining precision when adding and multiplying, and I was wondering if there might be still more different ways for sine and cosine functions. If so, is the precision of cos(a) different from the precision of sin(a) - except at pi/4, and (5/4)*pi? What about at (3/4)*pi and (7/4)*pi?
No; i know what relative precision is, i wanted something of an abosolute precision (such as pie or sqrt(2))
i wanted a way to get the trigonometric lines of any angle in a nice clean formula such as: f(x)= x^2 but for cos or sin
There are many approximation formulae out there, here are some classics:
**broken link removed**. Note that you can't get absolute precision, but you can get precision as good as the floating point number you are using to represent the answer.
Hi,
For sin(x)^2+cos(x)^2=y, y can only be equal to 1. It's not a general
equation for y like y=2*x+1 or something like that.
If you make the precision of sin(a) different than cos(a) then you
no longer have sin and cos, you have something else.
What is your purpose for making the precision different?
BTW, if we want to prove those identities for t=tan(x/2)
instead of tan(x/2) we would substitute cos(x/2)/sin(x/2) and
reduce the result. The result would be sin(x) or cos(x) depending
on which of those two equations in t were chosen.
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