Ironically, a sinusoidal wave, i.e., the plane-wave solution of Maxwell's equations for a free em. field,
\vec{E}(t,\vec{x})=\vec{E}_0 \cos(\omega t-\vec{k} \cdot \vec{x}), \quad \vec{k} \cdot \vec{E}_0=0, \quad \omega=c |\vec{k}|
cannot be realized in nature. That becomes immediately clear when you try to calculate the total energy of the electric field, which is infinity, and since we don't have an infinite amount of energy available, we can never create such a plane wave in the strict sense.
Of course, according to Fourier's theorem you can write any free-field solution in the form of a Fourier integral
\vec{E}(t,\vec{x})=\int_{\mathbb{R}^3} \frac{\mathrm{d}^3 \vec{k}}{(2 \pi)^3} \tilde{\vec{E}}(\vec{k}) \exp[-\mathrm{i} |\vec{k}| c t+\mathrm{i} \vec{k} \cdot \vec{x}], \quad \vec{k} \cdot \tilde{\vec{E}}(\vec{k})=0.
I've used the (complex) exponential form of the Fourier integral, because it's more convenient than the cos-sin form, but is of course equivalent.
