THE HONG KONG POLYTECHNIC UNIVERSITY Computer Programming $($ENG$2002)$ Class $5$ Programming Test $1$

Name: $q,$ Student No$.q,$

A$.$ Instructions

Create a folder yyyyyyyy$,$ where yyyyyyyy stands for your student ID number $($omitting the last letter $\text{'}$D$\text{'})$ under PolyU Home Drive $(P$: $).$ All your Jupyter Notebook files should be stored under this folder yYYYyYyy$.$ Note: this drive and folder location MUST be strictly followed. Do NOT use anv other locations.

At the beginning of each Python program file, add a comment to show your student ID and name.

This paper comprises $3$ parts. You may use a new Jupyter Notebook file for each part. Create the files under the folder you created in Step $1.$

It is an open$-$book test; any documents, online or offline, can be consulted during the test.

Your programs need to be well commented. Lacking comments will result in down$-$grading.

Your programs need to have a good structure. Never write a long program without calling functions.

Do NOT use any techniques that were not mentioned in the lessons. Also, do NOT call a function recursively, i$.$e$.,$ call functionA $()$ inside functionA $().$

Do NOT import any library module $($except math$).$

Save your files frequently to avoid any accidental loss of data.

After the test, upload the three Jupyter Notebook files under the yYyYyyYy folder to Blackboard as attachments. $($Click the switch "Browse Local Files".$)$

Time allowed: $1$ hour $45$ minutes.

B$.$ The Programming Task

Background

It is given that the cosine function can be approximated by a series of summation and subtraction of many terms:

$cos(x)={\displaystyle \underset{k=0}{\overset{}{}}}(-1{)}^k(\frac{x^{2k}}{(2k)!})$~~$1-\frac{x^2}{21}+\frac{x^4}{4321}-\frac{x^6}{654321}+\frac{x^8}{87654321}-$cdots

where $kx(2k)2k(2k)(2k)(2k-1)$cdots$21cos(-1\mathrm{.}571)=-0\mathrm{.}00020367$~~$1-$ubrace$(\frac{(-1\mathrm{.}571{)}^2}{21}$ubrace${)}_{\{\begin{array}{ccc}\text{:}[& \text{F}\text{i}\text{r}\text{s}\text{t}\text{t}\text{e}\text{r}\text{m}& ]\\ k=1\end{array}}+$ubrace$(\frac{(-1\mathrm{.}571{)}^4}{4321}$ubrace${)}_{\{\begin{array}{ccc}\text{:}[& \text{S}\text{e}\text{c}\text{o}\text{n}\text{d}\text{t}\text{e}\text{r}\text{m}& ]\\ k=2\end{array}}-\frac{(-1\mathrm{.}571{)}^6}{654321}+$cdotsq$-3\mathrm{.}1416.It$ should $be$ noted that $kis$ the term number, $xis$ measured $in$ radian, and $(2k)!isto$ find the factorial $of2k,$ which $is$ given $by(2k)(2k)(2k-1)$cdots$21.$ For example,

$cos(-1\mathrm{.}571)=-0\mathrm{.}00020367$~~$1-$ubrace$(\frac{(-1\mathrm{.}571{)}^2}{21}$ubrace${)}_{\{\begin{array}{ccc}\text{:}[& \text{F}\text{i}\text{r}\text{s}\text{t}\text{t}\text{e}\text{r}\text{m}& ]\\ k=1\end{array}}+$ubrace$(\frac{(-1\mathrm{.}571{)}^4}{4321}$ubrace${)}_{\{\begin{array}{ccc}\text{:}[& \text{S}\text{e}\text{c}\text{o}\text{n}\text{d}\text{t}\text{e}\text{r}\text{m}& ]\\ k=2\end{array}}-\frac{(-1\mathrm{.}571{)}^6}{654321}+$cdots

$Q1.$ Create a new Jupyter Notebook file with the name $"PT1Q1".On$ starting, the application should cal function showMenu $()$ that shows the following main menu:

$[t]$ Get a term $in$ cosine function

$[a]$ Get the terms $in$ cosine function

$[c]$ Get cosine $ofan$ angle $in$ radian

$[q]$ Quit

State your choice $(t,a,c,orqto$ quit$)$:THE HONG KONG POLYTECHNIC UNIVERSITY Computer Programming $($ENG$2002)$ Class $5$ Programming Test $1$

Name: $q,$ Student No$.q,$

A$.$ Instructions

Create a folder yyyyyyyy$,$ where yyyyyyyy stands for your student ID number $($omitting the last letter $\text{'}$D$\text{'})$ under PolyU Home Drive $(P$: $).$ All your Jupyter Notebook files should be stored under this folder yYYYyYyy$.$ Note: this drive and folder location MUST be strictly followed. Do NOT use anv other locations.

At the beginning of each Python program file, add a comment to show your student ID and name.

This paper comprises $3$ parts. You may use a new Jupyter Notebook file for each part. Create the files under the folder you created in Step $1.$

It is an open$-$book test; any documents, online or offline, can be consulted during the test.

Your programs need to be well commented. Lacking comments will result in down$-$grading.

Your programs need to have a good structure. Never write a long program without calling functions.

Do NOT use any techniques that were not mentioned in the lessons. Also, do NOT call a function recursively, i$.$e$.,$ call functionA $()$ inside functionA $().$

Do NOT import any library module $($except math$).$

Save your files frequently to avoid any accidental loss of data.

After the test, upload the three Jupyter Notebook files under the yYyYyyYy folder to Blackboard as attachments. $($Click the switch "Browse Local Files".$)$

Time allowed: $1$ hour $45$ minutes.

B$.$ The Programming Task

Background

It is given that the cosine function can be approximated by a series of summation and subtraction of many terms:

The user is expected to enter a character of $\text{'}t\text{'},\text{'}a\text{'},\text{'}c\text{'}$ or $\text{'}$