Wikipedia defines the instantaneous frequency of a function $s(t)$ by derivative of $\frac{1}{2\pi}\arg(s(t)+i\widehat{s}(t))$ where $\widehat{s}$ is the Fourier transform of $s$ and $i$ is imaginary one.
Then in another page defines the instantaneous frequency of a function $\sin (s(t))$ by derivative of $\frac{1}{2\pi}s(t)$.
Are these two definitions the same (or compatible)?