Program For Calculating Sin Using Taylor Expansion Not Working?

Question

I\'m trying to write some code that\'ll calculate the value of sin(0.75) using the Taylor expansion, and print each iteration until the absolute difference between the value cal

Answer 1

It looks too obvious to most people so no-one even wanted to answer, but it should be said explicitly

The condition x - sin(0.75) < 10**(-6) is obviously not true when x very different from sin(0.75), so the do while loop is never entered.

Also, as IanH commented 10**(-6) will give 0 because the result of the power of two integers is again an integer. The literal real number 10^-6 should be expressed as 1e-6.

If you change it to x - sin(0.75) > 1e-6 the loop will proceed, but it will run forever, because your iteration is wrong. Taylor series works differently, you should compute

y = 0
y = y + x**1/1!
y = y - x**3/3! 
y = y + x**5/5!
y = y - x**7/7!
...

and so on, which is a very different kind of loop.

Try this one:

program taylor
 implicit none
 real :: x = 0.75
 real :: y, fact
 integer :: sgn, i

 fact = 1
 sgn = 1

 y = 0

  do i = 1, 10, 2
    y = y + sgn * x**i / fact
    fact = fact*(i+1)*(i+2)
    sgn = -sgn
  end do
  print *, y, sin(x)
end program taylor