def fact(n):
if n <= 1:
return 1
else:
return n * fact(n - 1)
def taylor_sin(x, m):
value = 0
eps = 1e-18
for i in range(1, m + 1):
value += ((-1) ** (i - 1)) * ((x ** (2*i-1)) / fact(2*i-1))
if i == 1:
last = value
#print(i, last, value, abs(value-last))
else:
#print("i=",i, "last=",last, "value=", value, "a-b=",abs(value-last))
if abs(value-last) < eps:
return value
else:
last = value
def taylor_cos(x, m):
a = 1
count = 1
for k in range(1, m):
if count%2 != 0:
a -= (x**(2*k)) / fact(2*k)
else:
a += (x**(2*k)) / fact(2*k)
count += 1
return a
def sin(x):
return taylor_sin(x, 300)
def cos(x):
return taylor_cos(x, 100)
x = 1
#print("sin(",x ,")=", sin(x, 100))
print("sin(%d)= %.12f"%(x, sin(x) ))
#print("cos(%d)= %.12f"%(x, cos(x) ))
