Creating Trig Tutorial: Are You Ready to Master Trigonometry?

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The discussion revolves around a user tasked with creating an interactive trigonometry tutorial using Macromedia Flash, despite initially misunderstanding the project requirements. The tutorial will cover the history of trigonometry, introduce sine and cosine functions, and demonstrate how to graph these functions in Excel without using the COS function. The user seeks advice on incorporating witty elements and historical anecdotes into the tutorial, as well as technical assistance with importing video files into Flash. Additionally, there are inquiries about animation techniques and pronunciation of mathematical terms for narration. The overall goal is to produce an engaging and educational resource for students learning trigonometry.
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[EDIT: Scroll down to see my subsequent postings if you are too lazy to read this.]


I am desperately in need of help.

Some weeks ago, I inadvertently signed up to do a mathematics project, not realising that it really was about designing tutorials (preferably interactive) for students. I was having my exams at the time, so I did not read the application form thoroughly, but just glanced through it (we were doing three two-hour long papers a day!). I swear that there was nothing in the form that said anything about designing tutorials, but the mathematics teacher wants me to do just that for my project.

The original project that I had in mind was suggested by DamnedCharming here on PF and it can be found here: https://www.physicsforums.com/showthread.php?t=16435

It's really just about numerically integrating \frac{d^2x}{dt^2} = -x to get a x = cos (t) curve.

I have no choice but to design a tutorial for trigonometry, because I have already chosen the title (Introduction to Trigonometry and Deriving the Cos(x) and Sin(x) curve) two weeks ago and cannot change it. My teacher wants me to use the Macromedia Flash program so I'm learning that from basic right now.

I was thinking of maybe doing the tutorial (in Macromedia Flash of-course) with a little bit of trig-related history, introducing the sine and cosine functions and the tangent function, but then concentrating more on the sine and cosine functions, and then eventually using calculus to show them how a cosine or sine curve can be drawn in Excel(without using the COS function they have). It's a little impractical not to use the COS function in Excel, but this method IS an alternative even though it is not as accurate.

I'm trying to make my tutorial as witty as possible, and I'll also shoot a video of myself for the intro. Is importing a .mov or .avi file into Flash possible? Does anyone know any interesting Trigonometry-related history?

I would appreciate it if anyone could suggest any witty lines or analogies to use in this tutorial
 
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Chen provided this link http://www.phy.ntnu.edu.tw/java/shm/shm.html

I was wondering how I could draw something similar to the animation with Flash. Please if you have any files you think might help me out, please PM me and I'll provide you with my e-mail address. Thanks a lot.
 
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How do you pronounce De Moivre? I'm going to be narrating this whole movie so I need a bit of help on pronouncing names.
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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