Phasors, complex numbers, trig. question

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SUMMARY

The discussion focuses on the mathematical problem of aggregating the expression "cosx + 2cos^2(x/2)" using phasors, complex numbers, or trigonometric identities. It was clarified that the term "cos" should be interpreted as "cis," where cisθ = cosθ + isinθ. Participants agreed that replacing cosines with cis is necessary for solving the problem effectively, and using the exponential form e^{iθ} may simplify the calculations.

PREREQUISITES
  • Understanding of phasors and their application in wave interference
  • Knowledge of complex numbers, specifically the cis notation
  • Familiarity with trigonometric identities and transformations
  • Basic skills in manipulating exponential functions in the context of complex analysis
NEXT STEPS
  • Study the properties and applications of phasors in wave mechanics
  • Learn how to convert between trigonometric functions and their complex exponential forms
  • Explore the use of trigonometric identities in simplifying expressions
  • Investigate advanced topics in complex analysis, particularly Euler's formula
USEFUL FOR

Students studying physics or engineering, mathematicians dealing with wave functions, and anyone interested in the application of complex numbers in trigonometry.

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Homework Statement


Two "waves", characterized by cosx and cos^2(x/2) interfere. Using phasors or complex numbers or trigonometry as necessary, aggregate "cosx + 2cos^2(x/2)" - i.e. rewrite as a single cosine.

Homework Equations



I was told that there is an error in the way this questions was written and that cos is supposed to be cis

cisθ = cosθ + isinθ

The Attempt at a Solution



I don't know what to do. Am I supposed to replace all of the cosines in the original problem with cis?
 
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If that was what you were told, then yes, that is what you should do. Of course, [itex]cis(\theta)= e^{i\theta}[/itex] and that might be easier to use.
 

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