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using findroot for multiple functions


I need to solve multiple equations varying one parameter.  I am able to do
this if I vary the parameter in equal steps, but I have a list of numbers
that I need to plug in.  Here is an example because my description
probably is not very clear:

Here is an example of what works:

Table[t /.FindRoot[(t-a)*Sin[t+a] + Sin[t-a]*Cos[t+a], {t,0}],[a,1,10,.5]

My problem comes in because I want have a list of values that are not in
equal steps.  I have tried the following with no success:

list = {1, 3.4, 99.1,100,109}
ReplaceAll[[FindRoot[(t-a)*Sin[t+a] + Sin[t-a]*Cos[t+a],{t,0}],a-> list]

If anyone has an idea on how I can get this to work, please let me know.

Thanks,
Amy Sommer



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