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

AI Thread Summary
The discussion focuses on expressing the sinusoidal function 8.5sin(290t+325) in different forms, specifically as C1cos(wt) + C2sin(wt). Various equivalent expressions are provided, including 8.5cos(290t-125) and -8.5cos(290t+55). Participants suggest using trigonometric identities for simplification, particularly the identity A cos(wt) + B sin(wt) = (A^2 + B^2)^(1/2) cos(wt + tan^-1(-B/A)). However, an alternative approach using the sine addition formula is recommended for easier conversion. The conversation emphasizes the flexibility of expressing sinusoidal functions in multiple forms.
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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