The correct answer is: A. $f$ has frequency components at 0 and $${1 \over {2\pi }}Hz$$
The function $f(t) = sin2t + cos 2t$ is the sum of two sine waves, one with frequency $2\pi$ and one with frequency $0$. The frequency of a sine wave is the number of times it goes through a full cycle in one second. The frequency of a sum of two sine waves is the sum of the frequencies of the two sine waves. Therefore, the frequency of $f(t)$ is $2\pi + 0 = 2\pi$.
The frequency components of a function are the frequencies of the sine waves that make up the function. The frequency components of $f(t)$ are $2\pi$ and $0$.
Here is a graph of $f(t)$:
[asy]
unitsize(1 cm);
draw((0,-1.2)–(0,1.2));
draw((0,0)–(12,0));
real g(real t) {
return sin(2pit) + cos(2pit);
}
draw(graph(g,0,12),red);
label(“$t$”, (12,0), E);
label(“$f(t)$”, (0,1.2), N);
[/asy]
As you can see, the graph of $f(t)$ is a sine wave with frequency $2\pi$. This is consistent with the fact that the frequency components of $f(t)$ are $2\pi$ and $0$.