position of spike in the spectrum of a sin wave
A sinusoid is the sum of two complex exponentials ("negative" and "positive" frequency) so that their imaginary parts cancel out each other:

$$cos(f \cdot t) = \frac{1}{2} \left( exp(f \cdot t \cdot i) + exp(-f \cdot t \cdot i) \right)$$

The Fourier Transform decomposes your input into a weighted sum of complex exponentials. Therefore, you get to see two pulses in the spectrum. One at -f and another at +f, basically. Typically, the "negative half" of the spectrum is located after the positive half because in discrete signals there is no difference between -f Hz and fs-f Hz where fs is the sampling frequency. So, your FFT result's ordering is 0 Hz to almost fs Hz where you can think of the second half as the negative portion of the spectrum.

Since real-valued signals have an imaginary part of zero, you'll notice that the Fourier Transform of real-valued signals always exhibits a symmetry between negative and positive frequencies with a certain kind of phase relationship (same amplitude and negated phase) so that the complex exponentials' imaginary parts cancel between negative and positive frequency.

Complex-valued signals are more general in that their spectra don't have to be symmetric around 0 Hz. The imaginary part helps you distinguish between positive and negative frequencies:

$$exp(f \cdot t \cdot i) = cos(f \cdot t) + i \cdot sin(f \cdot t)$$

As you can see above, the sign of f does not change the real part. But it does affect the sign of the imaginary part.