The Maclaurin series expansion for the sine function is:

https://drive.google.com/file/d/0BwwLB5_Kft3dYXprbm1KT0xoMWs/view?usp=sharing

where x is in radians. This function can be used to approximate the sine of x with increasing accuracy as terms are added to the summation. Write a function that accepts two scalar inputs (in order):

1. A value for x (in radians).
2. The number of series sums, N , to use in the series approximation of sin(x).

Your function should generate the following three outputs (in order):

1. A column vector of the first N series summations. Consider the first summation to be x-x^3/3!.
2. A column vector of the magnitude (i.e. absolute value) of the approximate relative error values associated with the first N series summations. Note the "previous approximation" for the first value in this vector will be x.
3. A column vector of the true relative error values associated with the first N series summations. Use MATLAB's built-in sine function to compute the true value for this error calculation.

Note: The first two test cases test the results for the first and second series sums respectively to aid in your debugging process.