High Tech Trig!

1. High Tech Trig! ? Project Entry Event The Final Product The Driving Question The Project Scenario Unit Goals Project Timeline Project Steps Resources

2. High Tech Trig! Entry Event • This project requires you and your team to master the basics of trigonometry and then apply these fundamentals to applications in the real world. • Watch the following videos and document your initial thoughts as to what you think about how it relates to the project. Share these thoughts with the rest of your project team. WARNING: Prepare for a goofy overload! • http://www.youtube.com/watch?v=PQyETUg2_I0 • http://www.hrmvideo.com/catalog/applications-of-trigonometry • http://www.youtube.com/watch?v=qXxTu0fg4_8 • http://www.youtube.com/watch?v=SgpB6cSaeh4 • http://www.youtube.com/watch?v=PIWJo5uK3Fo Return to MAIN

3. High Tech Trig! Project Scenario You and your team are part of a company that has a business model to use the a special tool that your R&D group developed and patented to measure any dimension a client may need, including the height of anything over 3 meters tall. This not only can save your clients time and money, but also allows them to measure the dimensions of tall objects or difficult to reach objects without endangering the lives of their employees. Return to MAIN

4. High Tech Trig! Project Scenario The special “trig tools” are a set of remote controlled drones that are relatively small and nimble, allowing them to hover at a fixed point of interest. They are fitted with analyzers and targets that will accurately measure any interior angle or side length of a virtual triangle. The only draw-back is that they can only measure up to three parameters at any one time (two side lengths and an angle, two angles and a side length, three side lengths, etc.). You know, however, that with trigonometry, you can simply program the tools’ analyzers and on-board computers to calculate the other parameters you need, making measurement of all angles and lengths unnecessary.

5. High Tech Trig! Project Scenario The initial market research you have done indicates that you have a wide range of potential customers in the private sector market in areas of surveying, construction, geography, transportation, astronomy, and the movie industry, as well as government applications that range from the Park Service to the military.

6. High Tech Trig! Project Scenario • Your company has three versions of its trig tools: • The least expensive model is restricted to just right triangles and will work for applications in which the customer needs help finding other parameters of a right triangle when either two side lengths are known or a single side length and an angle is known. • The middle option will do the same as the cheaper version, but also find parameters for any non-right triangle, when at least two angles and a single side are known or two sides and their enclosed angle are known. • The high-end model will do the same as the other two, but is primarily intended for covert applications, where coding of the results is necessary, as well as applications that relate right triangles to circles (or visa versa).

7. High Tech Trig! Project Scenario Your team’s eventual task is to develop a detailed marketing plan that shows your potential clients how your trig tools specifically meet the needs of various real-world applications that address the types of scenarios described above. You will ultimately act as the company’s hot-shot sales representatives with the job to showcase this marketing plan to potential customers at an industry trade show. Return to MAIN

8. High Tech Trig! Driving Question How can your sales team develop a captivating marketing plan that highlights the expertise of your company and its ability to use its trig tools to meet an array of customer demands. ? Return to MAIN

9. High Tech Trig! Final Product • The first part of your final product is developing a name and logo for your company and its high-tech trig tools (i.e. a name for each model listed in the project scenario). • Because your sales team has been hand-picked by the executives of your company to develop and present a marketing plan for your trig tools at an industry trade show, you and your teammates will need to verify that you are subject matter experts in the area of basic trigonometry. This ensures that you can correctly answer any question a potential customer may have! • For the purposes of this part of the project, you and your team should use scaffolding activities, tutorials, examples from the texts, other on-line information, etc. to develop this expertise against all goals and essential questions of this unit of study. Note that students in Category 2 or 3 will need to complete their required number of scaffolding activities in this step. Return to MAIN

10. High Tech Trig! Final Product • As members of your sales team verify mastery of their trigonometry knowledge to each other, you will begin developing your marketing plan. • The plan must address at least two unique and different applications for each of the three models of the trig tools your company has to offer. Detailed supporting documentation must be available and used to justify each scenario: • Applications for the least expensive model should include at least one example where a missing side must be found and one case where a missing angle must be found. • Applications for the middle option must include one case that uses the Law of Sines and one case that uses the Law of Cosines. • The high-end applications should include one “covert” example where interpretation of trigonometric identities is necessary and one example that makes use of one of the three basic trigonometric function graphs.

11. High Tech Trig!Final Product • Your marketing plan must ultimately be produced in a way that highlights your team’s creativity and depth of knowledge of the mathematics needed for your company to thrive! • The plan must also specifically reference your answer to the project’s driving question and provide enough real-world examples to convince any potential client that they should do business with your company. • While at the trade show, your team’s marketing plan display must be attended by at least two of your company’s sales representatives at all times. At least one other member of your sales team must be “trolling” the trade show, gathering intelligence and looking for trade secrets from his/her competition (these roles must be rotated throughout the time of the trade show).

12. High Tech Trig!Final Product • Other final product requirements: • Your marketing plan may consist of videos, mini-presentations, flyers, props, etc., but must at least include a professional looking, tri-fold display appropriate for a trade show that will be attended by your potential customers. • All team members must develop business cards to hand out to prospective customers and other interested parties. • Everyone in the group should dress and act professionally during the entire trade show. • All team members must participate equally in the presentation (at their displays and trolling). • As group members troll the other displays, they will be asked to assess the thoroughness of each of their peer displays. The results of this peer assessment will be used to identify at least three teams that will earn high mastery on the project.

13. High Tech Trig! Project Extension • Your team (or individuals on your team) may choose to extend the project beyond the minimum standards presented in the project scenario with one or more of the following examples: • Showing an exceptional level of creativity, excitement, and depth of knowledge by all team members at the trade show. • Creating more than the minimum number of application examples for one or more of the trig tool models (including an application that makes use of the area of a triangle and/or makes use of the relationship between radian measure and degree measure). • Making use of particularly complex, but accurate applications for all models of the trig tool (especially the high-end model). • Being one of the three top teams, as chosen by one’s peers and other trade show attendees (i.e. TCEC staff, other judges, etc.). • Proving that your team is completely ready for the trade show, with supporting documentation for all application examples at least a week before the trade show date. • Explicitly being able to use this project to prove mastery of all goals and answer all essential questions by all team members. Return to MAIN

14. High Tech Trig! Unit Overview This unit provides an introduction to trigonometry, one of the most powerful subject areas in the field of mathematics. The unit will be done with students working in PBL teams, as specified by this document. Each team will follow the PBL process and is ultimately responsible for producing a final product that ensures mastery of the specific goals for this unit. Return to MAIN

15. High Tech Trig!Project Goals • Goal 1– CCSS Math Content Standards SRT.C.6, 7, & 8: Use trigonometric ratios solve right triangles in applied problems, explain and use the relationship between the sine and cosine of complementary angles, and understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. • Essential Questions: • Can I define and evaluate the six trigonometric ratios (sin, cos, tan, cot, csc, and sec)? • Am I able to solve problems using trigonometric ratios (i.e. make use of SOH CAH TOA to find all the missing parts of a right triangle)? • Can I approximate the values of trigonometric ratios using a calculator? • Am I able to solve equations involving trigonometric inverse functions (e.g. sin-1q)? • Can I relate the right triangle trig ratios to the Pythagorean Theorem ?

16. High Tech Trig!Project Goals • Goal 2 – CCSS Math Content Standards SRT.C.9, 10, & 11:Apply trigonometry to general triangles to understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles and find the area of a triangle using trigonometry. • Essential Questions: • Can I use the Law of Sines and Law of Cosines to solve triangles when given any combination of three parameters (AAS, ASA, or SSA)? • Can I use non-right triangle trigonometry to model and solve real-world problems? • Can I derive the formula A = 1/2 ab sin(C) for the area of a triangle, by drawing an auxiliary line from a vertex perpendicular to the opposite side?

17. High Tech Trig!Project Goals • Goal 3– CCSS Math Content Standards F-IF.4 & 7: For standard trigonometric functions (sin, cos, and tan), describe the function and interpret key features of its graph, such as intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. • Essential Questions: • Can I explain the relationship between a triangle trigonometry and the unit circle? • Can I relate degree measure to radian measure on the unit circle? • Am I able to derive basic trigonometric identities using the unit circle? • Do I know the domain restrictions of the basic trigonometric functions (i.e. knowing where division by zero and negative radicands can generate restrictions)? • Can I relate the unit circle to the standard trigonometric functions and describe the characteristics of the graphs for each?

18. High Tech Trig!Big Ideas Trigonometric laws and functions such as sine, cosine, and tangent are used to do all types of computations for finding various lengths and angles of triangles, one of the most ubiquitous shapes in history and in our society. While knowledge of trigonometry is used extensively in engineering and the sciences, it is also very important to areas such as graphics & drafting, navigation, design, land surveying, electronics, and construction. Return to MAIN

19. High Tech Trig! Project Steps • The project steps for this and all PBL projects for this class are found in the “Generic PBL Guidelines – IM2” document: • http://sdrv.ms/17u80N4 ? Return to MAIN

20. High Tech Trig! Resources • PBL Rubrics: All rubrics and other PBL documents needed for this project are found on the Moodle Website (Main Page): • http://ccvs.cherokee.k12.nc.us/mod/folder/view.php?id=3456 • Scaffolding Activities: Activities you and your team will need in order to master the goals for this project are found under the Type I and Type II folders in the Moodle website for Unit 5 (a cross reference of activities vs. goal is also found on this site): • http://ccvs.cherokee.k12.nc.us/course/view.php?id=29 • Tutorials: An extensive set of tutorials for each goal of this unit may be found on the Moodle website for this unit. • http://ccvs.cherokee.k12.nc.us/course/view.php?id=29 Return to MAIN

21. High Tech Trig! Project Timeline: Week of…Item: November 16, 2013: Project Kick-off November 16 to January 13: Scaffolding Activities & Work On Project Solutions to Master all Unit Goals. Week of January 13, 2014: Project Completion / Mock Presentations Week of January 20, 2014: Deadline for Project Presentations & Reflection (Redosas needed) ? Return to MAIN