Sine function equation calculator

PowerUp!Instructional UnitUnit Plan Title:Do The WaveDeveloped By:Lorie JohnstonAcademic Vocabulary:Sinusoidal, sine wave, amplitude, frequency, phaseshift, vertical shift, linear change, inverse circular functions, inverse trigonometric functions, arcsin, arccos, arctan, secant, cosecant, cotangent, reciprocal trigonometric functions and harmonics.Grade Level: 11 & 12Length of Unit:4 weeksScience/MathStandard(s):What standards will provide the focus for this unit?1.S D Content Standards 2004 (Mathematics):9-12.A.3.2AStudents are able to create formulas to model relationships that are algebraic, geometric, trigonometric and exponential.2.S D Content Standards 2004 (Mathematics):9-12.A.4.4AStudents are able to apply properties and definitions of trigonometric, exponential and logarithmic functions.3. S D Content Standards 2004 (Mathematics):9-12.A.4.5AStudents are able to describe characteristics of nonlinear functions and relations.Essential Questions: What essential questions will focus this unit?1. Why is the study of sine waves important?2.What influence does knowledge of sine and cosine have on the study of music?Content:What topics do studentsneed to know?Skills:What should students be able to do?Students will need to know: 1. How to graph circular trigonometric functions of sine, cosine and tangent.2. How to apply transformations to graphs of circular trigonometric functions and determine the equation of the graphs.3. How to graph circular inverse trigonometric functions such as secant, cosecant and cotangent.4. How to evaluate arcsin, arc cos and arctan.5. How to solve trigonometric equations.Students will need to be able to:1. Graph circular trigonometric functions and inverse circular trigonometric functions.2. Write equations showing changes in amplitude, period and phase shift for sine, cosine and tangent graphs.3. Create trigonometric graphs for data showing sinusoidal trends.4. Determine the value of the arcsin, arccos and arctan.5. Solve problems using trigonometric functions.
Assessment(s): What evidence will show that students understand?Performance Tasks, Projects:Worksheets, Graphing calculator activities and computer investigation, Presentation of Ferris Wheel and Sine Graph project.Unit Circle on Geometer’s Sketchpad.Quizzes, Tests, Academic Prompts:Achievement Series Trigonometric Functions PretestAchievement Series Trigonometric Functions Post test Chapter TestInformal observations/discussions/interviews:SynchronEyesStudent Self-Assessment:Evaluation rubric for Ferris Wheel project.Planning the Learning Experiences: What teaching and learning experiences will equip students to demonstrate the targeted standards?Mathematical modeling:Use of Windows Journal and graphing calculator to work examples.Graphing Calculator Activity: Use of graphing calculator and TI Interactive to create graphs of trigonometric functions.Fathom Activity: Use the internet to collect data on dates for marriages in Canada. Use the information to create sine and cosine graphs toshowing the trend for marriagesof Youth Cohorts in Canada. Internet Project: Create 3 paper graphs showing personal biorhythms according to internet data. Use the graphs to add the sine functions and create a graph showing the sum of the sines on TI Interactive.Hands on Lab Activity:Activity which models sound waves and a weight bouncing on a spring---collect data and graph using the graphing calculator. Worksheet:Practice the problems and concepts.Geometer’s Sketchpad Project:Create a Ferris Wheel using Geometer’s Sketchpad. Make a table to compare the angle above or below the horizontal for each chair and calculate the vertical or horizontal distance. Use this information to make a sine or cosine graph using TI Interactive. Determine the equation of the sinusoidal graph.