Classroom Resource

Desmos: Graphing the Sine Function Using Amplitude, Period, and Vertical Translation

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

In this classroom resource from Desmos, students will build a visual understanding of amplitude, period, and phase shift with an introduction to trigonometric graphing. They can use this understanding to find models for given graphs of the sine function. The resource could also be used to help teach a lesson on trigonometric graphs. The resource includes sample student responses and a teacher's guide.

Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics

MA19.A2.35

Choose trigonometric functions (sine and cosine) to model periodic phenomena with specified amplitude, frequency, and midline.

Unpacked Content

UP:MA19.A2.35

Vocabulary

  • Trigonometric functions
  • Periodic phenomena
  • Amplitude
  • Frequency
  • Midline

Knowledge

Students know:
  • Key features of trigonometric functions (e.g., amplitude, frequency, and midline).
  • Techniques for selecting functions to model periodic phenomena.

Skills

Students are able to:
  • Determine the amplitude, frequency, and midline of a trigonometric function.
  • Develop a trigonometric function to model periodic phenomena.

Understanding

Students understand that:
  • Trigonometric functions are periodic and may be used to model certain periodic contextual phenomena.
  • Amplitude, frequency, and midline are useful in determining the fit of the function used to model the phenomena.
Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics

MA19.A2.20

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions.

Unpacked Content

UP:MA19.A2.20

Vocabulary

  • Polynomial function
  • Logarithmic function Trigonometric (sine and cosine) function
  • Reciprocal function
  • Radical function
  • Period
  • Midline
  • Amplitude
  • End Behavior
  • Intervals
  • Maximum
  • Minimum
  • Horizontal Asymptote
  • Vertical Asymptote
  • Inverse functions

Knowledge

Techniques for graphing.

  • Key features of graphs of functions.

    • Skills

    Students are able to:

    • Identify the type of function from the symbolic representation.
    • Manipulate expressions to reveal important features for identification in the function.
    • Accurately graph any relationship.
    • Find the inverse of a function algebraically and/or graphically.

    Understanding

    Students understand that:

    • Key features are different depending on the function.
    • Identifying key features of functions aid in graphing and interpreting the function.
    • A function and its inverse are reflections over the line y = x.

    Body

    1. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions. a. Graph polynomial functions expressed symbolically, identifying zeros when suitable factorizations are available, and showing end behavior. b. Graph sine and cosine functions expressed symbolically, showing period, midline, and amplitude. c. Graph logarithmic functions expressed symbolically, showing intercepts and end behavior. d. Graph reciprocal functions expressed symbolically, identifying horizontal and vertical asymptotes. e. Graph square root and cube root functions expressed symbolically. f. Compare the graphs of inverse functions and the relationships between their key features, including but not limited to quadratic, square root, exponential, and logarithmic functions.
    Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics

    MA19.A2.20b

    Graph sine and cosine functions expressed symbolically, showing period, midline, and amplitude.
    Link to Resource
    https://teacher.desmos.com/activitybuilder/custom/56b3e682b884dbd81be6ed09

    CR Resource Type

    Learning Activity

    Resource Provider

    Desmos
    Accessibility
    License

    License Type

    Custom

    Custom License Type (URL)

    https://www.desmos.com/terms

    Comments or Notes

    Desmos's mission is to help every student learn math and love learning math. Teachers can explore and enjoy Desmos collections of free digital math activities that include:

    • Meaningful feedback by showing students what their answers mean, then give them the opportunity to improve their thinking and revise their work.
    • Collaboration by using devices to connect students, not to isolate them. Students see their classmates' thinking. They ask each other questions and create challenges for each other.
    • Invites students to solve challenging problems using the tools they already have.

    If the teacher does not have an account, he/she will need to create a FREE account. (More information on how Desmos works can be found at Getting Started.)

    Once the teacher has selected an activity to run, he/she will need to click on the "Create Class Code" button. This will generate a unique class code and a link to view the dashboard. (More information can be found at Creating a Class Code.) Every new activity will need a new class code in order to start a session. Students cannot start the activity until they have the class code - so sessions can be started days, hours, or mere minutes before you plan to run the activity. When the teacher is ready to have students start, have the students go to student.desmos.com and enter the class code. Although it is not required, Desmos strongly encourages students to sign in with their Desmos Student Account. Signing in allows students to resume and view their past activity work.

    yvetteakridge
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