"This question is ill-posed as"
0.93969
"is a polynomial of degree 0 which does the job."
"A calculator calculates the value of cos(x) through the Taylor"
"series."
"The Taylor series of cos(x) is : "
1 - x^2/(2!) + x^4/(4!) - x^6/(6!) + ...
"What you need to know is that the angle you fill in this series"
"must be in radians. So 20° = "pi/9 = 0.349..." rad."
"To have a fast convergent series |x| must be smaller than 1,"
"by preference smaller than 0.5 even."
"We have luck as this is the case. In the other case we would"
"have to use goniometric identities to make the value smaller."
"We must have :"
(pi/9)^n/(n!) < 0.001 ", n as small as possible"
=> n=4
"This is the fault term so, "x^4/(4!)" does not have to be"
"evaluated even, so we need only the first two terms :"
1 - x^2/2 = 1 - (pi/9)^2/2 = 0.93908
"Clearly, the error is less than "10^-3" or "0.001"."
"You might ask yourself further how we get the value of "pi"."
"This can be done, among others, through the Taylor series of"
"arctan(x) as arctan(1) = "pi/4 => pi = 4*arctan(1)"."
"But there are other quicker (better convergent) series to"
"calculate "pi"."
