Objectives: Learn how to write a convergent algorithm using Taylor series and how to use global variables

For Taylor Series, Read the Taylor documents included with this Lab. Study the series to see how it converges. Note that

for these Trig functions, Taylor converges quickly. The number of terms will vary based on the size of the angle and the

size of epsilon.

For this program you will write a script and two functions, sine and cosine using Taylor series $($NOTE: you can use any

name except the Matlab function names sin and cos for these functions$).$ Refer to ME$1101$ Taylor Series DOC. The

purpose of this program is to test your sine and cosine function to insure it solves for sin and cos accurately.

CONCEPTS:

e$=10^-$ k$.].$

You will gradually increase k to improve the accuracy of your functions sine and cosine compared to the MATLAB sin and

cos so that your function$$s results match closely the MATLAB sin and cos functions. When you match the MATLAB sin

and cos functions accuracy, freeze k$.$ For Lab $6$B set the value of k to this value.

You will use csine as a counter for your sine function and ccosine as a counter for your cosine function. the variables

csine and ccosine will be used to count how many cycles your sine and cosine functions require to converge to an

accurate answer. Your results of Sine and Cosine, k$,$ and csine for Sine and ccosine for Cosine will be recorded in the

Excel sheet TEST TAYLOR.

Requirements:

$1.$ Write a Script that cycles until user stops it$.$

$2.$ Ask the user to input k a global variable in the script, k will then be used in both of your $2$ functions. Epsilon in

each function will be $10^-$k$.$ So$,$ by increasing k you will be improving the accuracy of your functions.

$3.$ Ask the user for an angle in radians.

$4.$ Using the angle the user entered, call both your sine and cosine function, as well as the MATLAB sin and cos

functions with the same angle. Compare the results for a range of angles between $0$ and $.$ Pick at least $4$

different angles across this range. Adjust your input of k until you get answers close to the MATLAB functions.

$5.$ Write your two functions for sine and cosine using Taylor series.

Here is a general outline

The purpose of the Lab is to test your sine and cosine functions. Comparing results to the MATLAB sin and cos built in

functions. This exercise is to have you write your sine and cosine functions using the Taylor series algorithm.

This is also an exercise in using global variables. There are $3$ global variables: k the exponent for e which equals $10^-$k$.$

Script:

Loops until user stops $($WHILE$)$

Declare the globals k$,$ csine, ccosine in the script.

Input value for k

Input angle to calculate the sine and cosine of this angle $($in radians$)$ using your sine and cosine function as well as

MATLABs sin and cos function $($built it functons$).$ By increasing the absolute value of k you make e smaller. As e gets

smaller you should be able to approach and eventully equal the MATLAB sin and cos values for the angle.

With k set and angle input finished

Call four functions with the same angle as defined

Your sine

Your cosine

MATLAB sin e$.$g$.$ Ms$=$sin$($angle$)$;

MATLAB cos

At this point don$$t reloop yet rather take the data and enter the information into the TEST TAYLOR sheet given in

CANVAS. After a good number of runs use the data from the TEST TAYLOR sheet to set k$.$

Loops until user stops $($WHILE$)$

You will use your sine and cosine function with k fixed to solve Lab $6$B$.$

end of Script

function your sine function

global variables k and csine

function your cosine function

global variables k and ccosine

end

ONE Script and $2$ Functions per requirements