Is There a Trick to Remembering the Trigonometric Functions?

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SUMMARY

This discussion focuses on understanding trigonometric functions—sine (sin), cosine (cos), and tangent (tan)—and their application in physics and mathematics. Participants emphasize the importance of visualizing right triangles and using mnemonic devices like "SOH CAH TOA" to remember the relationships between the sides of triangles. Key insights include the consistent use of cosine for the x-axis and sine for the y-axis, with exceptions noted for specific applications such as Snell's Law. The conversation also highlights the effectiveness of drawing diagrams and practicing with real-world examples to build confidence in using these functions.

PREREQUISITES
  • Understanding of right triangles and their properties
  • Familiarity with basic trigonometric functions: sine, cosine, tangent
  • Knowledge of polar coordinates and their relevance in trigonometry
  • Ability to use mnemonic devices for memorization
NEXT STEPS
  • Study the derivation and application of the Pythagorean theorem in trigonometry
  • Learn how to apply trigonometric functions in physics problems, particularly in vector analysis
  • Explore the use of scientific calculators for computing trigonometric values
  • Investigate advanced topics such as the unit circle and its relationship to trigonometric functions
USEFUL FOR

Students in mathematics and physics, educators teaching trigonometry, and anyone seeking to improve their understanding of trigonometric functions and their applications in real-world scenarios.

  • #31
Mark44 said:
You are aware, I hope, that the etymology you posted about SOH CAH TOA was completely made up.

We have adopted tags recently that are intended to do just that. B - beginner, I - intermediate, A - advanced. We haven't used them much here in the math sections, but they are used a fair amount in the physics sections.

Yeah. I just noticed 'em a few days ago and came across the explanation. In regards to the fictional nature of Soh Cah Toa the Indian Chief, it was meant to extend the absurdity of the device to increase its effectiveness. World-class mnemonists memorize insane amounts of information with silly vignettes they picture in their minds eye. In my opinion, there should be many more devices to use... medical students live and die by them. As for this being a 'B', all I can say is:

Limit of the differential quotient - slope of the tangent line - mu. Can we let this exchange die now?
 
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  • #32
The story of the Native American should be considered fiction. It's a pun.

SOH CAH TOA

Soak a toe (ah?)
 

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