The series expansion (级数展开式) of sine function at a given x using n terms (项) is

这个附件的图。。。
(1) Write an M-file named “sine.m” which contains a function. The function computes the
value of sine function using the above expansion at a given x using n terms. In other
words (换句话说), the function sine(x,n) returns (返回) the value of the expansion at x
and the value is calculated using n terms.
(2) Matlab has a built-in (内建) sine function named “sin” which computes the value of sine
function at a given x. As you can imagine (想象), the values obtained by using theexpansion may not be the same with the results returned by the sin function used by Matlab. See the data in the following table for an example.
The number of n    Sin(π/4)    Sine(π/4,n)
        1                        0.707106… 0.785398…
    2                        0.707106… 0.704652…
    3                        0.707106… 0.707143…
    4                        0.707106… 0.707106…
    As you may have noticed from the table, for a given point π/4, the larger the number n is,
the closer the values obtained by using the expansion are to the actual values calculated
by the sin function in Matlab. Now a question rises: in order to achieve (达到) a certain
degree of accuracy (精确度), how many terms should be used in the expansion in
approximating (近似计算) the value of sine function?
To answer this question, write another M-file named “computeN.m” which finds the
number n in order to meet a required accuracy for a given point x. At some point in this
file, you should call (调用) the function in sine.m explicitly.
(3) Write a third M-file named “plotGraphs.m” which has a function taking the n as input and
plots both sin(x)-x and sine(x,n)-x on the same graph. The variable x should take the
values from -2π to 2π with the step length less than 0.1. Remember to add title, labels and
legend to the graph properly. Call this function from the function in computeN.m, so that
each time computeN(x,δ1) is executed, a graph of the two curves is plotted.
Hint: You may need to slightly (稍微地) change the function in sine.m to make it adapts
the cases that x is a vector.
(4) Run computeN(2, 10e-6) in the command window of Matlab and observe the difference
between the two curves: sin(x)-x and sine(x,n)-x.

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