Modeling with Sinusoidal Functions
Student Guide
Assignment Summary
For this assignment, you will use sinusoids to model mathematical and real-world problems.
Background Information
Data sets that are cyclical, harmonic, oscillating, or periodic can be modeled with sinusoidal functions.
Finding key features such as minimum, maximum, amplitude, period, and frequency are helpful in
determining a sinusoidal model. Recall that the general forms of equations of sinusoids can be in these
forms: y = a sin(b(x – c)) + d or y = a cos(b(x – c)) + d.
Assignment Instructions
For this project, you are expected to submit the assignment (Parts 1 and 2) at the end of this document.
Step 1: Prepare for the performance task.
a) Read through the guide before you begin so you know the expectations for this assignment.
b) If there is anything that is not clear to you, be sure to ask your teacher.
a) If your word processing program has an equation editor, you can insert your equations here.
Otherwise, print this activity sheet and write your answers by hand.
Step 2: Complete Parts 1 and 2 in the Assignment section of this document.
a) Read all directions carefully.
b) Complete each task.
c) Insert images or screenshots of graphs when needed. Be sure that all graphs or screenshots
include appropriate information such as titles, labeled axes, etc.
d) Be sure to show all your work. You will be given partial credit based on the work you show and
the completeness and accuracy of your explanations
e) Consider underlining and circling important components in the problems.
Step 3: Evaluate your project using this checklist.
If you can check each box below, you are ready to submit your project.
Have you answered all questions in Part 1 and Part 2?
Have you shown your work?
Did you include an image or screenshot of a graph when requested?
Are all your equations correct? Be sure to check your formatting carefully.
Step 4: Revise and submit your project.
a) If you were unable to check off all of the requirements on the checklist, go back and make
sure that your project is complete. Save your project before submitting it.
b) Your teacher will give you further directions about how to submit your work. You may be
asked to submit your responses through the virtual classroom, email it to your teacher, or print
it and hand in a hard copy.
c) Congratulations! You have completed your project.
Copyright © Edgenuity Inc.
, Student Guide (continued)
Assignment
Part 1: Write mathematical equations of sinusoids.
1. The following sinusoid is plotted below. Complete the following steps to model the curve using the
cosine function.
a) What is the phase shift, c, of this curve? (2 points)
b) What is the vertical shift, d, of this curve? (2 points)
c) What is the amplitude, a, of this curve? (2 points)
d) What is the period and the frequency factor, b, of this curve? (2 points)
Copyright © Edgenuity Inc.
Student Guide
Assignment Summary
For this assignment, you will use sinusoids to model mathematical and real-world problems.
Background Information
Data sets that are cyclical, harmonic, oscillating, or periodic can be modeled with sinusoidal functions.
Finding key features such as minimum, maximum, amplitude, period, and frequency are helpful in
determining a sinusoidal model. Recall that the general forms of equations of sinusoids can be in these
forms: y = a sin(b(x – c)) + d or y = a cos(b(x – c)) + d.
Assignment Instructions
For this project, you are expected to submit the assignment (Parts 1 and 2) at the end of this document.
Step 1: Prepare for the performance task.
a) Read through the guide before you begin so you know the expectations for this assignment.
b) If there is anything that is not clear to you, be sure to ask your teacher.
a) If your word processing program has an equation editor, you can insert your equations here.
Otherwise, print this activity sheet and write your answers by hand.
Step 2: Complete Parts 1 and 2 in the Assignment section of this document.
a) Read all directions carefully.
b) Complete each task.
c) Insert images or screenshots of graphs when needed. Be sure that all graphs or screenshots
include appropriate information such as titles, labeled axes, etc.
d) Be sure to show all your work. You will be given partial credit based on the work you show and
the completeness and accuracy of your explanations
e) Consider underlining and circling important components in the problems.
Step 3: Evaluate your project using this checklist.
If you can check each box below, you are ready to submit your project.
Have you answered all questions in Part 1 and Part 2?
Have you shown your work?
Did you include an image or screenshot of a graph when requested?
Are all your equations correct? Be sure to check your formatting carefully.
Step 4: Revise and submit your project.
a) If you were unable to check off all of the requirements on the checklist, go back and make
sure that your project is complete. Save your project before submitting it.
b) Your teacher will give you further directions about how to submit your work. You may be
asked to submit your responses through the virtual classroom, email it to your teacher, or print
it and hand in a hard copy.
c) Congratulations! You have completed your project.
Copyright © Edgenuity Inc.
, Student Guide (continued)
Assignment
Part 1: Write mathematical equations of sinusoids.
1. The following sinusoid is plotted below. Complete the following steps to model the curve using the
cosine function.
a) What is the phase shift, c, of this curve? (2 points)
b) What is the vertical shift, d, of this curve? (2 points)
c) What is the amplitude, a, of this curve? (2 points)
d) What is the period and the frequency factor, b, of this curve? (2 points)
Copyright © Edgenuity Inc.
