Fortran error when calculating cosx - fortran

Question

I was assigned the following problem:
Make a Fortran program which will be able to read a degree[0-360] checking validity range(not type) and it will be able to calculate and print the cos(x) from the following equation, where x is in radians:
cos(x)=1-x^2/2! + x^4/4!-x^6/6!+x^8/8!-...
As a convergence criteria assume 10^(-5) using the absolute error between two successive repeats (I suppose it means do's).
For the calculation of the ! the greatest possible kind of integer should be used. Finally the total number of repeats should be printed on screen.
So my code is this:
program ex6_pr2
implicit none
!Variables and Constants
integer::i
real*8::fact,fact2 !fact=factorial
real,parameter::pi=3.14159265
double precision::degree,radiants,cosradiants,s,oldcosradiants,difference !degree,radiants=angle
print*,'This program reads and calculates an angle`s co-sinus'
print*,'Please input the degrees of the angle'
read*,degree
do while(degree<0 .or. degree>360) !number range
read*,degree
print*,'Error input degree'
cycle
end do
radiants=(degree*pi/180)
fact=1
fact2=1
s=0
cosradiants=0
!repeat structure
do i=2,200,1
fact=fact*i
fact2=fact2*(i+2)
oldcosradiants=cosradiants
cosradiants=(-(radiants)**i/fact)+(((radiants)**(i+2))/fact2)
difference=cosradiants-oldcosradiants
s=s+cosradiants
if(abs(difference)<1e-5) exit
end do
!Printing results
print*,s+1.
end program
I get right results for angles such as 45 degrees (or pi/4) and wrong for other for example 90 degrees or 180.
I have checked my factorials where I believe the error is hidden (at least for me).
Well I created another code which seems unable to run due to the following error:FUNCTION name,(RESULT of PROJECT2_EX6~FACT),used where not expected,perhaps missing '()'
program project2_ex6
implicit none
integer(kind=3)::degrees,i,sign
integer::n
double precision::x,err_limit,s_old,s
real,parameter::pi=3.14159265359
print*,'This program calculates the cos(x)'
print*,"Enter the angle's degrees"
read*,degrees
do
if(degrees<0.or.degrees>360) then
print*,'Degrees must be between 0-360'
else
x=pi*degrees/180
exit
end if
end do
sign=1
sign=sign*(-1)
err_limit=1e-5
n=0
s=0
s_old=0
do
do i=1,n
end do
s=(((-1.)**n/(fact(2.*n)))*x**(2.*n))*sign
s=s+s_old
n=n+1
if(abs(s-s_old)<1e-5) then
exit
else
s_old=s
cycle
end if
end do
print*,s,i,n
contains
real function fact(i)
double precision::fact
integer::i
if(i>=1) then
fact=i*fact(i-1)
else
fact=1
end if
return
end function
end program

Answer 1

Although it is your homework, I will help you here. The first thing which is wrong is ýour factorial which you need to replace with
fact = 1
do j = 1,i
fact = fact*j
enddo
second it is easier if you let your do loop do the job so run it as
do i=4,200,2
and predefine cosradians outside the do loob with
cosradiants = 1-radiants**2/2
additionally you need to take into account the changing sign which you can do in the loop using
sign = sign*(-1)
and starting it off with sign = 1 before the loop
in the loop its then
cosradiants= cosradiants+sign*radiants**i/fact
If you have included these things it should work (at least with my code it does)