Trigonometric Functions Calculation and Graphing Project

PLEASE NOTE: THE PREVIEW VERSION OF THIS PRODUCT IS THE ACTUAL "STUDENT VERSION" AND DOES NOT INCLUDE ANY OF THE ANSWERS TO THE PROBLEMS. THE "TEACHER VERSION" INCLUDES DETAILED ANSWERS TO ALL OF THE PROBLEMS FOR THE PROJECT.

This project activity involves the calculation, graphing and coloring of the basic sine and cosine trigonometric functions/equations. I have my Algebra 2, Math 3 and Precalculus students complete this project toward the end of the unit on trigonometric functions. As noted in the TpT "Preview" section of this product covers all tranformations of the sine and cosine function except for the phase shift of the functions.

A total of eight (8) functions are provided that require the students to calculate the following for each one:

• Amplitude, Period and Midline
• Transformation Descriptions
• Function Domain and Range (all 3 formats)
• X-Y Intercepts

A series of very organized calculation sheets are provided for the students to calculate the above information for each function. Once these calculations are complete, the students will list the results on the Trigonometric Function Summary Table. This is followed by the completion of eight (8) separate Trigonometric Equation X-Y Coordinate Point Tables by the students to facilitate their graphing of each function. The 5-Point Graphing Method is reviewed in detail for use by the students to determine the coordinates to properly graph for each function. These points are plotted on the furnished graph grid for each of the functions/equations and a smooth curve is drawn for each. Finally the various sections formed by the intersecting lines of the plotted graphs are colored to provide an interesting "stained glass effect" final product. It should be noted that an alternative to manual graphing is also reviewed (i.e., use of the Desmos online graphing calculator).

This activity can be completed by students working individually; but, given the amount of calculations and graphing involved, I have my students work in pairs or groups to complete the project in a more timely manner. It usually takes two, 1-1/2 hour class periods to completely finish all parts of the activity with some of the final graph coloring also being assigned as homework.

This project activity package is an MS Word file and includes the following sections and appendices:

• Part A - General Introduction
• Part B - General Vocabulary
• Part C – General Trigonometric Function Curve Characteristics
• Part D – Function Transformations
• Part E – Phase Shift
• Part F - Domain, Range and X-y Intercepts of Trigonometric Functions or Equations
• Part G – Basic Steps to Graph Trigonometric Functions or Equations (including the 5-Point Graphing Method)
• Part H – Project Specific Guidelines
• Part I – Grading Rubric

• Appendix A - Student Worksheets including:
  • Trigonometric Equations Calculation Sheets
  • Trigonometric Function Summary Table
  • Trigonometric Equation X-Y Coordinate Point Tables

• Appendix B - Graph Grid (Blank Copy)
• Appendix C - Grading Rubric
• Appendix D - Teacher Answer Key Material including:
  • Completed Trigonometric Equations Calculation Sheets,
  • Completed Trigonometric Function Summary Table,
  • Completed Trigonometric Equation X-Y Coordinate Point Tables, and
  • Graph Grid (Blank Copy)
  • Graphs (1 - uncolored and 2 - colored)

As noted above two (2) completed, sample, colored graph grid examples are also included at the end of the activity package (one manual graph and one online Desmos-generated graph). There are 52 total pages in the package. The native MS Word file is included in the event the teacher desires to make any modifications to the activity to suit her or his classroom purposes.

Other MS PPT products for 6th Grade, 7th Grade, 8th Grade, Math 1, Math 2, Math 3, Algebra 1, Algebra 2, Geometry and PreCalculus curriculum topics can be reviewed and purchased under my TpT page titled: "Priceless Math".