<p>下面是一个改进版本:</p>
<pre><code>from math import radians
import sys
# version compatibility shim
if sys.hexversion < 0x3000000:
# Python 2.x
inp = raw_input
rng = xrange
else:
# Python 3.x
inp = input
rng = range
def type_getter(type):
def fn(prompt):
while True:
try:
return type(inp(prompt))
except ValueError:
pass
return fn
get_float = type_getter(float)
get_int = type_getter(int)
def calc_sin(theta, terms):
# term 0
num = theta
denom = 1
approx = num / denom
# following terms
for n in rng(1, terms):
num *= -theta * theta
denom *= (2*n) * (2*n + 1)
# running sum
approx += num / denom
return approx
def calc_cos(theta, terms):
# term 0
num = 1.
denom = 1
approx = num / denom
# following terms
for n in rng(1, terms):
num *= -theta * theta
denom *= (2*n - 1) * (2*n)
# running sum
approx += num / denom
return approx
def main():
print(
"\nProgram to approximate sin and cos."
"\nYou will be asked to enter an angle and"
"\na number of terms."
)
theta = get_float("Enter an angle (in degrees): ")
terms = get_int ("Number of terms to use: ")
print("sin({}) = {}".format(theta, calc_sin(radians(theta), terms)))
print("cos({}) = {}".format(theta, calc_cos(radians(theta), terms)))
if __name__=="__main__":
main()
</code></pre>
<p>请注意,由于麦克劳林级数以x=0为中心,接近0的θ值收敛得更快:<code>calc_sin(radians(-90), 5)</code>为-1.00000354258,而{<cd2>}为-0.444365928238(与-1.0的正确值相差约157000倍)。在</p>