Solving Arctan(x/y) - 90degrees

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SUMMARY

The discussion centers on proving the identity arctan(x/y) - 90 degrees = -arctan(y/x). This mathematical relationship is derived from the properties of right triangles, where arctan(x/y) represents the angle opposite side x. Subtracting 90 degrees results in the negative of the angle opposite side y, confirming the identity. This proof is particularly relevant for electrical engineering applications, as highlighted by a user who encountered it during an interview.

PREREQUISITES
  • Understanding of trigonometric functions, specifically arctangent.
  • Knowledge of right triangle properties and relationships.
  • Familiarity with angle measurement in degrees.
  • Basic concepts in electrical engineering related to angles and trigonometry.
NEXT STEPS
  • Study the properties of trigonometric identities in depth.
  • Explore applications of arctan in electrical engineering problems.
  • Learn about the unit circle and its relation to trigonometric functions.
  • Investigate the derivation of other trigonometric identities.
USEFUL FOR

Students and professionals in electrical engineering, mathematicians, and anyone interested in advanced trigonometric concepts and their applications.

flexifirm
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This is fun...

prove that:

arctan(x/y) - 90degrees = -arctan(y/x)

I had to do this recently for an electrical engineering problem (in an interview actually). It's ahrd at first, but once you picture things it comes fast.
 
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arctan(x/y) is the angle of a right triangle opposite x, so subtract 90 degrees and you're going to get the negative (since the first angle is less than 90) of the angle opposite side y.

Did you have to do that on the spot in your head? Sounds like a good question.

cookiemonster
 

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