DFT Vs DCT - spectrum differences
The DCT for a signal $x(t)$ on $[0,T]$ is roughly the same as the DFT for the function $x(|t|)$ on $[-T,T]$, that is, mirrored at the vertical axis. Since that function is even, all sine coefficients will be zero and can be removed from the result. 

Now $\sin(|t|)$ is different from $\sin(t)=-\sin(-t)$ for negative $t$, so the resulting coefficients will be quite unrelated. If the sampling interval ends at $t=T=2\pi$, the DFT will only exhibit one peak around frequency $f=\frac1{2\pi}$. 

But because of the kink at $t=0$ in $\sin(|t|)$, and a second at the end of the sampling interval, the DCT will exhibit a general background of size $f^{-2}$ in the coefficient for frequencies $f&gt;0$.