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Trigonometric Functions and Real Life Applications

Trigonometric Functions and Real Life Applications. Steven Alley. Analyze Learners.

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Trigonometric Functions and Real Life Applications

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  1. Trigonometric Functions and Real Life Applications Steven Alley

  2. Analyze Learners • My unit plan focuses on eleventh graders or anyone who has taken Algebra 1, Algebra 2, and Geometry. I assume that the students are proficient at algebra and are not well acquainted with trigonometric functions. Students will be on an equal playing field.

  3. State Objectives • M.O.T.3.1: Apply the right triangle definition of the six trigonometric functions of an angle in standard position given a point on the terminal side of the angle. • M.O.T.3.2: Convert angle measures from degrees to radians (and vice versa) and apply the concept to analyze the formula for arc length. • M.O.T.3.6: Identify a real life problem utilizing graphs of trigonometric functions. • M.O.T.3.9: Develop and test a hypothesis to find the area of a triangle given the measures of two sides and the included angle of the measures of three sides (Heron’s Formula) and use these formulas to finds total area of figures constructed of multiple shapes. • M.O.T.3.11: Create graphical and algebraic representations for performing vector operations and analyze these to solve real-world problems such as force analysis and navigation.

  4. 21st Century Learning and Technology CSO’s • 21.C.0.9-12.2.LS.1: Student engages in a critical thinking process that supports synthesis and conducts evaluation using complex criteria. • 21.C.0.9-12.2.LS.3: Student engages in a problem solving process by formulating questions and applying complex strategies in order to independently solve problems.

  5. Select Media and Material The students will be using the classroom computers. They will use graphing calculators. I will be using a Smartboard and students will interact with the Smartboard. I will also need worksheets and handouts. The students will be visiting websites as well.

  6. Websites Used • http://www.theteacherscorner.net (This website will be used to use the crossword puzzle maker as an assessment for the students.) • http://www.edhelper.com/trigonometry.htm (This website offers worksheets for the students on several areas of trigonometry.) • http://www.khanacademy.org (Videos on trigonometry that are used as tutorials.) • http://www.homeschoolmath.net/online/trigonometry.php (This website contains games and quizzes for students on trigonometry.)

  7. Utilize Media and Materials Day 1 Day 2 The lesson will help students to understand the relationship between degrees and radians by using a Smartboard. The students will convert degrees to radians and vice versa. Each child will perform a conversion on the Smartboard. • The lesson focuses on introducing sin(x), cos(x), tan(x), csc(x), sec(x), and cot(x). They will learn the ratios of the six functions, and I will give them a worksheet to do. The worksheet will cover the six functions and how to find amplitude, vertical shift, and period.

  8. Utilize Media and Materials Day 3 Day 4-5 Students will learn about how to map trigonometric functions to model real-world situations. They will work in groups to model navigation problems and share them with the class. Students will complete a crossword puzzle on the previous material. • The students will learn Heron’s Formula and where it came from. Why do we use it? They will watch a video on http://www.khanacademy.orgon Heron’s Formula. We will discuss arc length as well.

  9. Utilize Media and Material Day 6-8 Day 9-10 The students will give their presentations in front of the class. Students are encouraged to ask questions. • Students will be working on a group project that reflects the information from the unit. They will need a project board and a model of a real life situation. I will assist when needed.

  10. Require Learner Participation Students will be doing many projects that allow them to be creative and involved. Group work will help students to learn from each other and help motivate each other to stay on task. My assessment of the students is not some boring test.

  11. Evaluate and Revise • Day 1- (21.C.0.9-12.2.LS.1), (M.O.T.3.1): The students will share an answer in front of the class on trigonometric functions. • Day 2- (M.O.T.3.2): Students are assessed by doing conversions between degrees and radians on the Smartboard. • Day 3-5-(M.O.T.3.1), (M.O.T.3.2), (M.O.T.3.9), (21.C.0.9-12.2.LS.3): Students are assessed by a crossword puzzle on all definitions and share how they solved real world problems using graphical representation.

  12. Evaluate and Revise • Day1-5 (M.O.T.3.1), (M.O.T.3.2), (M.O.T.3.6), (M.O.T.3.9), (M.O.T.3.11): Students will be assessed overall by doing a project board on all presented material in the class.

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