Solving Sinusoids: Expressing 8.5sin(290t+325) in Different Forms

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SUMMARY

The discussion focuses on expressing the sinusoidal function 8.5sin(290t+325) in different forms, specifically as C1cos(wt) + C2sin(wt). Participants confirm that the function can be rewritten as 8.5cos(290t-125) or -8.5cos(290t+55). The use of trigonometric identities, particularly sin(a+b) and the transformation A cos(wt) + B sin(wt), is emphasized as a method for simplifying the expression.

PREREQUISITES
  • Understanding of trigonometric identities, specifically sin(a+b) and cos(a+b).
  • Familiarity with sinusoidal functions and their representations.
  • Basic knowledge of wave equations in physics or mathematics.
  • Ability to manipulate angles in radians for trigonometric functions.
NEXT STEPS
  • Study the application of trigonometric identities in wave equations.
  • Learn about the conversion between sine and cosine forms of sinusoidal functions.
  • Explore the implications of phase shifts in sinusoidal representations.
  • Investigate the graphical representation of sinusoidal functions and their transformations.
USEFUL FOR

Students in physics or mathematics, particularly those studying wave mechanics, as well as educators looking for effective methods to teach sinusoidal transformations.

Moneer81
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Homework Statement



Express 8.5sin(290t+325) as C1cos(wt)+C2sin(wt)


Homework Equations



The previous parts of the problem actually ask to find the wave equation itself and write it in different forms. So the above wave equation can also be expressed as 8.5cos(290t-125) or as -8.5cos(290t+55) etc.


The Attempt at a Solution



Can I use the following trig identity: A cos (wt) + B sin (wt) = (A^2 + B^2)^1/2 cos (wt + tan^-1 (-B/A)) ?
 
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It's easier than that. Use sin(a+b)=sin(a)*cos(b)+cos(a)*sin(b).
 

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