Understanding the Pythagorean Theorem's Ratios

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SUMMARY

The Pythagorean Theorem, expressed as a² + b² = c², directly leads to the derivation of trigonometric ratios: sine, cosine, and tangent. By defining 'a' as the length of the opposite side, 'b' as the length of the adjacent side, and 'c' as the hypotenuse, one can derive the trigonometric identities through division of these sides. This foundational relationship is essential for understanding trigonometry and its applications in various mathematical contexts.

PREREQUISITES
  • Understanding of basic geometry concepts
  • Familiarity with trigonometric functions: sine, cosine, tangent
  • Knowledge of the Pythagorean Theorem
  • Ability to perform algebraic manipulations
NEXT STEPS
  • Explore the derivation of trigonometric identities from the Pythagorean Theorem
  • Study the unit circle and its relationship to trigonometric functions
  • Learn about the applications of trigonometric ratios in real-world problems
  • Review Khan Academy's resources on trigonometry for visual and interactive learning
USEFUL FOR

Students learning trigonometry, educators teaching mathematical concepts, and anyone seeking to understand the relationship between geometry and trigonometric functions.

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Homework Statement



How does the pythagorean therm. give us sin cos tan and their recipr.? I don't understand how a^2 + b^2 = c^2 give you those ratios?

Homework Equations





The Attempt at a Solution

 
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The pythagorean theorem will give you the pythagorean identities if you let a=opposite side b=adjacent side, c= hypotenuse. You can derive all the pythagorean identities by dividing by the different sides.

You may want to skim over this http://mathsfirst.massey.ac.nz/Trig/TrigRatio.htm or even better take a look at the khan academy library of videos on trig.
 
Thank you.
 

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