MHB Trigonometry to Memorize and Trigonometry to Derive

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The discussion focuses on the importance of memorizing key trigonometric concepts while also recognizing the value of deriving certain formulas. The initial sheets contain essential trigonometric information deemed necessary for practical application, while the final sheet emphasizes derivation techniques. An updated TrigKnowledge file features improved visual representations of triangles and sine and cosine graphs, created using TikZ and Sage. The use of multiples of π/4 as tick markers on the x-axis enhances the clarity of the graphs. Overall, the thread highlights a balance between memorization and derivation in mastering trigonometry.
Ackbach
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In my career, so far, the first two pages of the attached sheets contains everything I've ever needed to have in my head; the last sheet contains most things I've had to derive. I hope you find this helpful.

https://www.physicsforums.com/attachments/910._xfImport

Comments and questions should be posted here:

http://mathhelpboards.com/commentary-threads-53/commentary-trigonometry-memorize-trigonometry-derive-4226.html
 

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I'm very excited to have updated my TrigKnowledge file. The two triangles are now drawn using tikz, and the two graphs of sine and cosine I drew using Sage. I figured out a way to get Sage to use multiples of $\pi/4$ as the tick markers on the $x$-axis, which greatly enhances this graph, in my opinion. Enjoy!
 
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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