# Calculate Sin(x), e^(x) , and Pi

This code allows you to calculate Sin(x), e^(x), and Pi without using any of the built-in VB functions

**Original Author:** Jonathon Lopez

### Assumptions

The way this code works is by using what is called Taylor Expansion. By generating a taylor series using derivatives it is possible to take the sum of the elements in that series to find such functions as Sin(x) and even Pi.

### Code

`'Sin(x) function`

'Note: this is in radians, not degrees

Public Function Sine(x as Double) as Double

Dim i As Integer, sum As Double: sum = 0

'Calculate the taylor expansion of sin

For i = 1 To 10

sum = sum + (((-1) ^ (i + 1)) * ((x) ^ (2 * i - 1)) / fact(2 * i - 1))

Next i

Sine=sum

End Function

'e^(x) function

Public Function e(x as Integer) as Double

Dim i As Integer, sum As Double: sum = 0

'Calculate the Taylor expansion of e

For i = 0 To 150

sum = sum + (x ^ i) / fact(i)

Next i

e=sum

End Function

'Pi function

Public Function pi() as Double

Dim i As Integer, sum As Double: sum = 0

For i = 1 To 15000

sum = sum + ((-1) ^ (i + 1)) * (1 ^ (2 * i - 1)) / (2 * i - 1)

Next i

pi = sum * 4

End Function

'Function that calculates factorials

Public Function fact(n As Integer) As Double

Dim i As Long, r As Double: r = 1

If n = 0 Then fact = 1

For i = 1 To n

r = i * r

Next i

fact = r

End Function

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