Trigonometry to Memorize and Trigonometry to Derive

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    Derive Trigonometry
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SUMMARY

The discussion focuses on the importance of memorizing and deriving key trigonometric concepts, as shared by a user who has compiled a comprehensive TrigKnowledge file. The file includes essential formulas and derivations, utilizing tools like TikZ for triangle illustrations and Sage for graphing sine and cosine functions. The user highlights the enhancement of graph readability by using multiples of $\pi/4$ as tick markers on the x-axis, showcasing effective visualization techniques in trigonometry.

PREREQUISITES
  • Understanding of basic trigonometric functions and identities
  • Familiarity with TikZ for creating geometric illustrations
  • Experience with SageMath for graphing mathematical functions
  • Knowledge of radians and their application in trigonometric graphs
NEXT STEPS
  • Explore advanced TikZ techniques for creating complex geometric figures
  • Learn how to effectively use SageMath for interactive graphing
  • Study the derivation of trigonometric identities and their proofs
  • Investigate the application of radians in various mathematical contexts
USEFUL FOR

Students, educators, and mathematics enthusiasts looking to enhance their understanding of trigonometry, particularly in memorization techniques and graphical representation of trigonometric functions.

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!
 

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