I have been writing code for a module I am making for my Discord Bot. I have been trying not to use any module as it is not helping in in importing stuff. So I thought I should write the code myself for both of them.
The problem here is that I don't really know how do we make them. I couldn't find them anywhere on the net as everywhere I only saw the use of math module which I don't want to use.
I don't know how do I work with them, so I want some help.
Thank You! :)
Using Taylor expansion you get an approximation up to the desired precision.
http://hyperphysics.phy-astr.gsu.edu/hbase/tayser.html
def pow(base, exponent):
return base ** exponent
def faktorial(n):
value = float(1)
for i in range(1, n+1):
value = value * i
return value
def cos(x):
x = x * 3.14/180
value = 1
sign = -1
n = 200 # precision
i = 2
while i < n:
value = value + (pow(x, i)/faktorial(i) * sign)
i = i + 2
sign = sign * -1
return value
def sin(x):
x = x * 3.14/180
value = x
sign = -1
n = 200 # precision
i = 3
while i < n:
value = value + (pow(x, i)/faktorial(i) * sign)
i = i + 2
sign = sign * -1
return value
pi = 3.1415926535897932384626433832795028841971 # Value of constant pi
def f(n): # Factorial Function
if n == 1 or n == 0:
return 1
else:
return n * f(n - 1)
def deg(x):
rad = x * pi/180
return rad
def sin(x): # Taylor Expansion of sinx
k = 0
sinx = 0
while x >= pi:
x -= pi
if pi > x > pi / 2:
x = pi - x
while k < 15:
sinx += (-1)**k * x**(2*k + 1) / f(2*k + 1)
k += 1
return sinx
def cos(x):
cosx = sin(pi / 2 - x)
return cosx
I improved the code now. Now it gives you accurate results of up to 14 decimal places. Also instead of writing full Taylor expression formula, I used a while loop to do that. While loop here acts as a summation function of maths. I also shorten the code inside cos(x). Instead of writing Taylor's expression here, I used a conversion formula of sinx to cosx. Which reduces the calculation process. I made a little change in the code. Now you can calculate sinx of huge number too with the same accuracy.
