|Lesson Plan ID:
Traveling Around The Unit Circle
This lesson is intended to review the key ideas associated with trigonometric functions.The design of this lesson provides a collection of reproducible activities to be used in a classroom setting where students have varied backgrounds / experience with trigonometric functions.
|MA2015(9-12) Algebra II with Trigonometry||39. Define the six trigonometric functions using ratios of the sides of a right triangle, coordinates on the unit circle, and the reciprocal of other functions. (Alabama) |
|MA2015(9-12) Algebra II with Trigonometry||40. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.* [F-TF5] |
Course of Study: Course: Pre Calculus
Grade Level: 12 Content Standard # 7, 9, 10, 11, 12
Convert between radians and degrees.
Find arc length.
Identify the periodicity and even-odd properties of trigonometric functions and explore various transformations upon those graphs.
Analyze the unit circle and generate the following: 0, 30, 45, 60, 90 degree angles.
Apply basic identities to solving trigonometric problems.
Practice ethical and legal use of technology systems and digital content.
Content Standard # 9
(Optional) National standards may be provided to assist teachers that may require them. Place a standard here to align the lesson with national or other standards.
Algebra: draw reasonable conclusions about a situation being modeled.
|Primary Learning Objective(s):
Students will use graphing calculators to aid in the discussion of graphs and periodicity of trigonometric functions.
Students will apply the problem-solving strategy of making a table to represent hand graphs.
|Additional Learning Objective(s):
Students will search the internet for examples of periodic functions in everyday life to compare and contrast them with the sine or cosine function.
|Approximate Duration of the Lesson:
|| 61 to 90 Minutes|
|Materials and Equipment:
Graphing calculators, graph paper, a linear measuring tool, note book and pencil.
|Technology Resources Needed:
Document camera, computers with Internet access.
Teacher should know basic trigonometric problem solving. Teacher should be familiar with the internet.
Students should have basic knowledge of trigonometric ratios and how to solve equations.
Students should know how to use the internet.
Class will begin with the review of the unit circle and its application to trigonometry. The focus will be on trigonometric functions of angles with irrational numbers that appear frequently in evaluating trigonometric functions.
This activity provides an opportunity for students to use their knowledge of the unit circle as they discover the measures of commonly used angles in trigonometry.
Note: The students will be divided into groups of four for this task. Teacher will lead them through the activity, beginning with the introduction through the evaluation.
2. Next, graphs and periodicity will be explored. Students will review the use of the graphing calculator. It will be noted that attention to the mode is relevant.
Using the TI-83/84 Graphing Calculator
Title: Calculator tutorial
Annotation: The students in this class come from many backgrounds. This website allows them to review the graphing calculator at their own pace and at the level of their knowledge.
Note: Students will select "Algebra, Trig, Calculus". Then select Trigonometry #8. Students will model exercises included in boxes.
3. Finally, the lesson extends the review of trigonometric functions by applying the problem-solving strategy Making a Table to graph them in the coordinate plane. Students will review the graph of the sine and cosine graph over the interval o < x < 2 π. Students will generate a set of values for (x, sin x) or for (x, cos x) and plot them on a coordinate system.
Using the TI-83/84 Graphing Calculator
URL : http://www.prenhall.com/divisions/esm/app/graphing/ti83/
Annotation : From the banner page, students will select "How to graph a function". Then select "Trigonometric Function". Students will model exercises included in boxes.
|Attachments:**Some files will display in a new window. Others will prompt you to download.
From the banner page, students select "Definition of Trig functions". Select "Recognize Functions 3". Select Applet Recognize functions 3. Select ‘Exercise' for detailed instructions. Students begin matching. Upon completion of matches, students will check answers.
Writing Connection: Students will describe real-world examples of trigonometric examples and explain the transformation of the resulting graphs. Examples: EKG waves; music sheets; etc.
Graphing calculators will be available for check out for home use as well as extra practice in a lab setting.
Extra Practice: Cool Math
Each area below is a direct link to general teaching strategies/classroom
for students with identified learning and/or behavior problems such as: reading
or math performance below grade level; test or classroom assignments/quizzes at
a failing level; failure to complete assignments independently; difficulty with
short-term memory, abstract concepts, staying on task, or following directions;
poor peer interaction or temper tantrums, and other learning or behavior problems.
|Presentation of Material
||Using Groups and Peers
|Assisting the Reluctant Starter
||Dealing with Inappropriate
Be sure to check the student's IEP for specific accommodations.
|Variations Submitted by ALEX Users: