Finding the first zero of e^{-20t}(5cos(40t) + 2.5sin(40t))

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Homework Statement



Find when this is "0" for the first time:

[tex]q(t) = e^{-20t} (5cos(40t) + \frac{5} {2} sin(40t))[/tex]


Homework Equations





The Attempt at a Solution



[tex]0 = e^{-20t} (5cos(40t) + \frac{5} {2}sin(40t))[/tex]

[tex]0 = (5cos(40t) + \frac{5} {2}sin(40t))[/tex]

[tex]cos(40t) = -\frac{1} {2}sin(40t))[/tex]


Is the best way to solve this perform interations?

Thanks
Sparky
 
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Discussion

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Iterations on what? You've basically solved it. Make that into [itex]tan(40t) = -2[/itex] and apply arctan. If you don't want a negative number in the argument, you can use the fact that arctan is an odd function.
 
Thanks Kreizhn,

I'm now embarrassed.

this was not seeing the forest for the trees.

I was about to open Excel and try different values of t until I got it to work out.

Thanks
Sparky