In a current lecture we had a quick visual introduction to the Fourier transform. It was explained that the Fourier transform turns a given wave into an approximative wave that consists out of cosine waves.
According to the explanation, the graphs below are the FT waves of sine and cosine. To my understanding the FT waves are equivalent to the "frequency spectrums" of the waves. And the frequency spectrum simply gives us the required consine waves with the frequency and its amplitude. The frequency of each wave is denoted on the x-axis and the amplitude on the y-axis.
If I understand it right, shouldn't the waves of sine cancel out since cosine is symmetric?
$$ amp *cos(freq \cdot x) + (-amp)*cos(-freq \cdot x) = 0$$