Discrete Fourier transform of even function
The real question is: what did you expect to see and why? I give you a few ideas and hints to help you understand the problem:


if you use the time domain data as shown in the top figure, then the first (left-most) point is interpreted as time index $n=0$ (there goes the cosine ...). Just look at the formula for the DFT and you'll see why.
Second, the implicit periodic continuation of the time domain data in the DFT means that you don't have a pure sinusoid (just append the first data point after the last data point and so on, and you'll see the problem). What you probably wanted is an integer number of periods in your time window (= DFT length), because then the periodic continuation will not change your nice sinusoid.