# MEM23004A Apply Technical Mathematics Indika Fernando Edwina Langford

Attach this cover sheet to each assessment task when submitted to your teacher.

Student Information

Student ID Number Contact Number

Student Name

Cluster/Unit Information

Department of Trades and Engineering Technology

National Unit Code

(s) National Unit Title(s) Teacher Name

MEM23004A Apply Technical Mathematics Indika Fernando Edwina Langford

Assessment Task Information

Title of Assessment Due Date

Assignment 2

Application for Extension (where applicable)

Extension Date for Submission Granted Until

STUDENT DECLARATION

? I have completed this assessment

? I am aware that penalties exist for plagiarism. Refer to http://www.swinburne.edu.au/corporate/registrar/plagiarism/index.html

STUDENT

SIGNATURE: DATE:

For electronic submissions only:

By typing your name in the student signature field, you are accepting the above declaration.

Trades and Engineering Technology

MEM23004A Apply Technical Mathematics – 2020 – Assignment 2

Assessment Topic/s Trigonometry and Sequences & series

Submission Details: Online submission via Canvas

Result Competent or Not Yet Competent

Assessment Description:

All assessment criteria listed below must be satisfactorily completed for the task to be assessed as satisfactory completed.

Additional Information:

This Assessment tasks covers following assessment criteria.

[RS1]-Solving mathematical problems using standard engineering software packages, and validating software results of simple examples analytically and/or graphically.

[RS3.2]-Graphing and analysing Trigonometry functions for solutions.

[RS4]Using the techniques of sequences and series to solve simple mathematical problems.

[RK1]software for mathematical analysis and graphical representations

[RK4] trigonometric equations

[RK5] sequences and series

Student Instructions

• This is a Competency based Assessment

• Read all the Instruction before attempting the assessment.

• Write your name and ID in the space provided in cover sheet, then signed and dated.

• Answer all the questions.

• Students are allowed to use class notes, scientific calculator, Microsoft Excel package, online mathematic software tools (eg. www.symbolab.com.au , https://www.symbolab.com/graphing-calculator) • Students must show all the working out for each question.

• Refer class notes and Activity sheets for theories and examples.

• Give the answer correct to two decimal places unless otherwise specified • Ensure that you submit assessments on or before the due date.

• Always retain a copy of your assessment tasks. (hard copy and soft copy)

• If you are found to be unsuccessful in particular question/s in the assignment you will be allowed resubmission. Your teacher will provide feedback regarding what you need to do to improve and will set a new deadline for the resubmission.

• Working outs on online calculators and Excel graphs must be save and email to your teacher.

• Teacher’s email address: Indika- gfernando@swin.edu.au, Edwina – elangford@swin.edu.au

Learning Outcome:

• [E1] Determine scope of technical mathematical techniques required for an engineering application

• [E2] Apply technical mathematical techniques to engineering applications

Results and Feedback

Assignment Results (First submission/ Re submission

• Competent

• Not Yet Competent – Re submission required

Feedback to students will be provided via Canvas feedback Rubric

Trigonometry Function

1) Following Sine wave graph demonstrates the Input voltage across a power line. Estimate the amplitude, period, frequency and phase shift (horizontal translation).

Amplitude Period Frequency Phase shift

2) Use the graphs of ?? = ???????? ?????? ?? = ???????? shown below to answer the following questions.

Find from the graphs, two approximate values of ?? between 0 ° ?????? 360° for which; a) sin ?? = 0.5

b) cos ?? = 0.4

c) sin ?? = -0.8

d) sin ?? = ????????

3) Solve following Trigonometry equations for 0 = ? = 3600 using an online calculator. (Take screenshots of your calculations and save and email to your teacher).

a) sin(2??) = 0.5

b) sin(??) = -0.8

c)

4) Compare the results in question 2 and 3 of sin(??) = -0.8 .

5) In an AC circuit with only a constant inductance, the voltage at time ?? (in seconds) is given by

?? = 10 sin(2????) Where 0 = ?? = 2

a) Determine the amplitude, period, Angular velocity and frequency of the function.

b) Calculate the voltage after 1.2 seconds.

c) Plot ?? as a function of ?? for 0 = ?? = 2 ,in the interval of 0.1.

(use Microsoft Excel or symbolab graphing calculator)

d) Use the graph to estimate the voltage after 1.2 seconds and compare with answer in part (b).

e) At what times is the voltage = 5V ? (use symbolab calculator) (give the answer in between 0 and 2 sec) (attached the screen shot of your workings on symbolab calculator)

Sequences and series

??2

6) Find the first six terms of ???? = 3 ??-1

7) The number of Laps that a swimmer swims each week follows an arithmetic sequence.

In the first week she swims 12 laps and in the 5th week she swims 24 laps.

a) Find the common difference between weeks

b) How many laps does she swim in the 15th week?

c) The total number of laps she swims in the first 15 weeks (S15)

d) Write an expression for S15 using summation notation [?15??=1(????)]

e) Use symbolab online calculator to evaluate the expression found in part c) and validate the answer found in part b) (attached the screen shot of your workings on symbolab calculator)

8) A pendulum swings a distance of 58 m initially from one side to the other. After first swing, each swing is only of the distance of the previous swing. What is the total distance covered by the pendulum in 12 swings?

3??

9) Evaluate (manually) :

Formula Sheet

1) Amplitude, Period, frequency and phase angle from Sine and Cosine curves

2) Amplitude, Period, Phase shift and vertical shift from Sine and cosine equations

3) Online Symbolab calculator URL www.symbolab.com.au

4) Convert Radian to Degree

5) Arithmetic Sequences

6) Geometric Sequences

7) Arithmetic Series

8) Geometric Series

Student Information

Student ID Number Contact Number

Student Name

Cluster/Unit Information

Department of Trades and Engineering Technology

National Unit Code

(s) National Unit Title(s) Teacher Name

MEM23004A Apply Technical Mathematics Indika Fernando Edwina Langford

Assessment Task Information

Title of Assessment Due Date

Assignment 2

Application for Extension (where applicable)

Extension Date for Submission Granted Until

STUDENT DECLARATION

? I have completed this assessment

? I am aware that penalties exist for plagiarism. Refer to http://www.swinburne.edu.au/corporate/registrar/plagiarism/index.html

STUDENT

SIGNATURE: DATE:

For electronic submissions only:

By typing your name in the student signature field, you are accepting the above declaration.

Trades and Engineering Technology

MEM23004A Apply Technical Mathematics – 2020 – Assignment 2

Assessment Topic/s Trigonometry and Sequences & series

Submission Details: Online submission via Canvas

Result Competent or Not Yet Competent

Assessment Description:

All assessment criteria listed below must be satisfactorily completed for the task to be assessed as satisfactory completed.

Additional Information:

This Assessment tasks covers following assessment criteria.

[RS1]-Solving mathematical problems using standard engineering software packages, and validating software results of simple examples analytically and/or graphically.

[RS3.2]-Graphing and analysing Trigonometry functions for solutions.

[RS4]Using the techniques of sequences and series to solve simple mathematical problems.

[RK1]software for mathematical analysis and graphical representations

[RK4] trigonometric equations

[RK5] sequences and series

Student Instructions

• This is a Competency based Assessment

• Read all the Instruction before attempting the assessment.

• Write your name and ID in the space provided in cover sheet, then signed and dated.

• Answer all the questions.

• Students are allowed to use class notes, scientific calculator, Microsoft Excel package, online mathematic software tools (eg. www.symbolab.com.au , https://www.symbolab.com/graphing-calculator) • Students must show all the working out for each question.

• Refer class notes and Activity sheets for theories and examples.

• Give the answer correct to two decimal places unless otherwise specified • Ensure that you submit assessments on or before the due date.

• Always retain a copy of your assessment tasks. (hard copy and soft copy)

• If you are found to be unsuccessful in particular question/s in the assignment you will be allowed resubmission. Your teacher will provide feedback regarding what you need to do to improve and will set a new deadline for the resubmission.

• Working outs on online calculators and Excel graphs must be save and email to your teacher.

• Teacher’s email address: Indika- gfernando@swin.edu.au, Edwina – elangford@swin.edu.au

Learning Outcome:

• [E1] Determine scope of technical mathematical techniques required for an engineering application

• [E2] Apply technical mathematical techniques to engineering applications

Results and Feedback

Assignment Results (First submission/ Re submission

• Competent

• Not Yet Competent – Re submission required

Feedback to students will be provided via Canvas feedback Rubric

Trigonometry Function

1) Following Sine wave graph demonstrates the Input voltage across a power line. Estimate the amplitude, period, frequency and phase shift (horizontal translation).

Amplitude Period Frequency Phase shift

2) Use the graphs of ?? = ???????? ?????? ?? = ???????? shown below to answer the following questions.

Find from the graphs, two approximate values of ?? between 0 ° ?????? 360° for which; a) sin ?? = 0.5

b) cos ?? = 0.4

c) sin ?? = -0.8

d) sin ?? = ????????

3) Solve following Trigonometry equations for 0 = ? = 3600 using an online calculator. (Take screenshots of your calculations and save and email to your teacher).

a) sin(2??) = 0.5

b) sin(??) = -0.8

c)

4) Compare the results in question 2 and 3 of sin(??) = -0.8 .

5) In an AC circuit with only a constant inductance, the voltage at time ?? (in seconds) is given by

?? = 10 sin(2????) Where 0 = ?? = 2

a) Determine the amplitude, period, Angular velocity and frequency of the function.

b) Calculate the voltage after 1.2 seconds.

c) Plot ?? as a function of ?? for 0 = ?? = 2 ,in the interval of 0.1.

(use Microsoft Excel or symbolab graphing calculator)

d) Use the graph to estimate the voltage after 1.2 seconds and compare with answer in part (b).

e) At what times is the voltage = 5V ? (use symbolab calculator) (give the answer in between 0 and 2 sec) (attached the screen shot of your workings on symbolab calculator)

Sequences and series

??2

6) Find the first six terms of ???? = 3 ??-1

7) The number of Laps that a swimmer swims each week follows an arithmetic sequence.

In the first week she swims 12 laps and in the 5th week she swims 24 laps.

a) Find the common difference between weeks

b) How many laps does she swim in the 15th week?

c) The total number of laps she swims in the first 15 weeks (S15)

d) Write an expression for S15 using summation notation [?15??=1(????)]

e) Use symbolab online calculator to evaluate the expression found in part c) and validate the answer found in part b) (attached the screen shot of your workings on symbolab calculator)

8) A pendulum swings a distance of 58 m initially from one side to the other. After first swing, each swing is only of the distance of the previous swing. What is the total distance covered by the pendulum in 12 swings?

3??

9) Evaluate (manually) :

Formula Sheet

1) Amplitude, Period, frequency and phase angle from Sine and Cosine curves

2) Amplitude, Period, Phase shift and vertical shift from Sine and cosine equations

3) Online Symbolab calculator URL www.symbolab.com.au

4) Convert Radian to Degree

5) Arithmetic Sequences

6) Geometric Sequences

7) Arithmetic Series

8) Geometric Series