sinusform

Sinusform is a term encountered in mathematics and signal processing that refers to representations built from sine-based components. In many mathematical contexts it overlaps with the trigonometric or polar form of complex numbers. A nonzero complex number z can be written in polar form as z = r(cos θ + i sin θ), where r is the magnitude and θ the argument. This form is equivalent to z = r e^{iθ} by Euler's formula, and the sine and cosine terms describe the projection of z onto the imaginary and real axes. The concept emphasizes the role of angles (phases) and magnitudes in the complex plane.

In the context of real-valued signals, a sine-based representation expresses a function as a sinusoid of the form f(t) = A sin(ωt + φ), with amplitude A, angular frequency ω, and phase φ. A sinusform may refer to a single sinusoid or to a sum of sinusoids used in Fourier-like decompositions. Such representations facilitate interpretation of frequency content and straightforward manipulation of amplitude and phase under addition and scaling.

Usage of the term varies by discipline; the standard, widely taught terminology is trigonometric or polar form for complex numbers, while 'sinusoidal form' or 'sine form' may be used informally in some courses. See also Euler's formula, polar coordinates, the complex plane, and Fourier series.