cos2ft

Cos2ft is a concise way to denote the mathematical function cos(2 f t), where f and t are real-valued variables. It represents a cosine with angular frequency ω = 2 f and can be interpreted as a single-frequency component at that frequency in signal processing or Fourier analysis. When f is interpreted as a frequency in Hz and t in seconds, cos(2 f t) uses an angular frequency of 2 f (some contexts instead write cos(2π f t)).

The basic properties of cos2ft include that it is periodic with period π / f for f ≠ 0, is an even function in t, and takes values in the interval [-1, 1]. If f = 0, cos2ft reduces to the constant value 1 for all t.

Several standard trigonometric identities apply. The double-angle form gives cos(2 f t) = 2 cos^2(f t) − 1 = 1 − 2 sin^2(f t). In exponential form, cos(2 f t) = (e^{i 2 f t} + e^{−i 2 f t}) / 2, reflecting its interpretation as the real part of a complex exponential with frequency 2 f.

Relation to other functions is notable: cos(2 f t) is the second harmonic of cos(f t). It arises, for example, when squaring a cosine or in the Fourier representation of periodic signals that include a second-frequency component.

Common applications include analysis and synthesis of periodic signals, harmonic content characterization, and modulation or demodulation contexts where a second-frequency term is present. An example value: if f = 1 Hz, cos(2 t) has period π seconds.