Final answer:
The assertion that the number of resolvable harmonics is equal to the number of data points is false. In reality, the number of uniquely determined harmonics is half the number of data points because each harmonic requires both a sine and a cosine component to be resolved.
Step-by-step explanation:
When a series of cosines and sines are used to represent a function, the number of frequencies or harmonics that can be resolved is not exactly equal to the number of data points provided. Rather, the number of independent frequencies that can be resolved is half the number of data points due to the need to resolve both the sine and cosine components for each frequency. The given series including terms like A1 sin (2πt/T) and B1 cos (2πt/T) can represent a function with multiple harmonics, but the number of harmonics that can be uniquely determined is limited by the available data points and the need for each harmonic to have a sine and a cosine component.
A sine function oscillates between +1 and -1 every 2π radians, and the wave function, or the y-position of the medium, oscillates between +A and -A, repeating every wavelength λ. This oscillation provides the simple harmonic motion seen in waves, which can also be represented using cosine functions with a phase shift, as indicated by the equation x(t): = A cos (ωt + φ). However, when analyzing Fourier series and signal processing, it's important to understand that the maximum number of unique harmonics that can be resolved is limited by the available data points.