Evaluate trig functions at infinity?

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SUMMARY

The discussion centers on the evaluation of trigonometric functions, specifically cosine and sine, at infinity in relation to Fourier integrals. It is established that the improper integrals of sin(x) and cos(x) from zero to infinity do not converge or diverge, indicating that cos(infinity) does not have a defined value. The graph of cosine oscillates indefinitely without approaching a specific limit as x approaches infinity, reinforcing the conclusion that evaluating these functions at infinity is not meaningful.

PREREQUISITES
  • Understanding of trigonometric functions, particularly sine and cosine.
  • Familiarity with the concept of limits in calculus.
  • Knowledge of Fourier integrals and their properties.
  • Basic graphing skills for trigonometric functions.
NEXT STEPS
  • Research the properties of Fourier integrals and their convergence criteria.
  • Study the behavior of trigonometric functions at infinity.
  • Explore the concept of improper integrals in calculus.
  • Learn about oscillatory functions and their limits.
USEFUL FOR

Mathematicians, physics students, and anyone studying calculus or Fourier analysis who seeks to understand the behavior of trigonometric functions at infinity.

AStaunton
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is it meaningful to evaluate cos and sin at infinity? I ask in relation to Fourier integrals...

ie does cos(infinity) have a value
 
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The improper integral of sin(x) or cos(x) from zero to inf does not converge or diverge
so you can't evaluate it.
 
AStaunton said:
ie does cos(infinity) have a value

You tell me. What does the graph of cosine look like? Is cos(x) going to approach a certain number as x approaches infinity?
 

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