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Which is the variable for amplitude in fourier transform equation?

In this Sinusoidual signal equation: Equation

I know that A_0 is to shift the signal up or down, and the A_n is for the amplitude. What I don't understand however is when this equation is transformed into Fourier transform equation, the variable for the amplitude goes missing?

This is the fourier transform equation: Fourier Transform Equation
Both a_n and b_n are variables for the phase. What about the variable for the amplitude?
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