VBA Sine Homework Assignment

Computation of Sin (x)
VBA Program
Submitted By
Student Name
Problem Statement
This VBA Program calculates the value of sin(x) from the series
The series may be represented as:
Assumptions
The absolute value of the terms in the series get smaller and smaller so the size of the last term used to find the sum, sin(x) will be used to decide when we have reached the desired accuracy. A finite number of terms may be used to calculate the approximate value of this infinite series.
Theory & Discussion
The infinite series or Maclaurin series of sin(x) is used to find estimate on values of the sine function at every point.
In order to use Taylor’s formula to find the power series expansion of sin x we have to compute the derivatives of sin(x):
Sin’ (x) = cos(x)
Sin’’(x) = − sin(x)
Sin’’’(x) = − cos(x)
sin(4)(x) = sin(x)
Since sin(4)(x) = sin(x), this pattern will repeat.
Further, we evaluate the function and its derivatives at 0:
sin(0) = 0
sin (0) = 1
sin(0) = 0
sin(0) = −1
sin(4)(0) = 0
The pattern is repeated. Therefore, the formula explains:
sin(x) = 0 + 1x + 0x2 + − 1 x3/3! + 0x4 + · · ·
sin(x) = x – x3/3! + x5/5! –x7/ 7! + · · ·
This shows that the addition and subtraction signs alternate and the factorials in the denominator grow big...