TI-nspire Activity Janine Williams, Mary Rose Landon Course Level: Advanced Algebra, Precalculus Time Frame: 2-3 regular (45 min.) class sessions Objectives: Students will... 1. Explore the Unit Circle, making conjectures about angles in each quadrant and their cosines, sines, and tangents. 2. Plot Unit Circle data and graph trig functions. 3. Connect findings to amplitude, period, and asymptotes of trig. graphs. 4. Compare features of the Unit Circle to properties of trig. functions. 5. Appreciate the cyclic nature of trig. functions and their graphs. Materials: UNITCIRCLE2, CIRCLEPROJECT files (NTS files) TI-nspire handhelds (class set) Student activity sheets Lesson Descriptions: Day #1 (1 day): This lesson provides an introduction to using the TI-nspire (so far they have only used basic calculator and graphing features) while investigating the Unit Circle. Students are asked to trace a point around the Unit Circle. They will capture data, entering (x,y) values of special angles 30, 45, 60, and 90 in each quadrant into a spreadsheet on the calculator. Students will discover (or re-discover ) that, for each angle θ, x = cos(θ), y = sin(θ), and y/x = tan(θ). They will also compare signs of these values in the four quadrants. Students will record (x,y) values on a copy of the circle and answer questions about the properties of the Unit Circle and the trig. functions.
Day#2 (1-2 Days) Today s activity is more involved and should take longer. But once the students open the CIRCLEPROJECT file on their handhelds, they will follow clear step-by-step directions. They should be able to... Recall yesterday s findings and connect (x,y) values on the Unit Circle to cosine, sine, and tangent of different angles. Use a spreadsheet to store the Unit Circle data for special angles in all four quadrants (0 to 360º). Plot scatter plots (after defining variables), and graph the cosine, sine, and tangent functions on their plots. Answer questions about the graphic features of the trig. functions, including period, amplitude, asymptotes, and the cyclic nature of their graphs. They will also connect this information to the domain and range of the functions. Summarize findings (connect Unit Circle to trig. functions and their graphs). Note: These activities may be used separately, as an introduction to trig. functions in Advanced Algebra, or as enrichment in Precalculus. Students in our classes seemed to benefit from the investigative, hands-on nature of the n-spire activities. Please feel free to contact Janine Williams or Mary Rose Landon with questions or comments regarding this activity. We teach Advanced Algebra (J. Williams) and Precalculus (M.R.Landon) at South Park High School in Buffalo, NY. jlwilliams@buffaloschools.org mlandon@buffaloschools.org
Explore Sine, Cosine, and Tangent on the Unit Circle Objectives: The cosine, sine, and tangent of an angle can be found on the Unit Circle. Today we will plot data and graph the curves for the trigonometric functions. Then you will analyze your graphs, answer questions, and summarize your findings. Directions: Open the file CIRCLEPROJECT on your TI-nspire. Use ctrl > to go to the next page. Follow each step and pause to answer questions. You may also write answers to questions on this sheet. Read pp 1.2 1.4. then look at Unit Circle on pg. 1.5. When you turn to the spreadsheet on pg. 1.6, type xval in the top cell of column B and hit Enter. Then enter yval in the top cell of column C, Enter. When you hit Enter, the calculator will fill the spreadsheet with the cosine data (x values).
Now follow the directions on pg 1.7, and create a scatter plot on pg 1.8. Use the menu button, then select the following: 3: Graph Type > 4: Scatter Plot Select angle for x and xval for y in your scatter plot. After graphing your scatter plot, Select 3:Graph Type 1: Function and graph f(x)=cos(x) Compare your graphs; answer questions on pg 1.9 (Write answers below): * * * Now follow directions on pg. 1.10 to draw a scatter plot on pg 1.11, using angle for x and yval for y. Then graph f(x)= sin(x) on the plot.
Answer questions on pg. 1.12: 1. Period: Amplitude: 2. Follow directions on pg. 1.14 to enter tangent data in your spreadsheet in column D. Ploy your scatter plot on pg. 1.15, using angle for x and tangent for y. Then graph the function f(x)=tan(x) on the plot. After looking at your graphs, answer the following questions (pg 1.16-1.17): *
* Summarize your findings. (see pg. 1.18): Summary: