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Tracing the y component of a circle while going around the circle results in a sine wave (red). Tracing the x component results in a cosine wave (blue). Both waves are sinusoids of the same frequency but different phases. A sine wave, sinusoidal wave, or sinusoid (symbol: ∿) is a periodic wave whose waveform (shape) is the trigonometric sine ...
The sine and the cosine functions, for example, are used to describe simple harmonic motion, which models many natural phenomena, such as the movement of a mass attached to a spring and, for small angles, the pendular motion of a mass hanging by a string. The sine and cosine functions are one-dimensional projections of uniform circular motion.
The cosine double angle formula implies that sin 2 and cos 2 are, themselves, shifted and scaled sine waves. Specifically, [ 27 ] sin 2 ( θ ) = 1 − cos ( 2 θ ) 2 cos 2 ( θ ) = 1 + cos ( 2 θ ) 2 {\displaystyle \sin ^{2}(\theta )={\frac {1-\cos(2\theta )}{2}}\qquad \cos ^{2}(\theta )={\frac {1+\cos(2\theta )}{2}}} The graph ...
The sine and tangent small-angle approximations are used in relation to the double-slit experiment or a diffraction grating to develop simplified equations like the following, where y is the distance of a fringe from the center of maximum light intensity, m is the order of the fringe, D is the distance between the slits and projection screen ...
Adding a sine wave (red) and a cosine wave (blue) of the same frequency results a phase-shifted sine wave (green) of that same frequency, but whose amplitude and phase depends on the amplitudes of the original sine and cosine wave.
A modulated wave resulting from adding two sine waves of identical amplitude and nearly identical wavelength and frequency. A common situation resulting in an envelope function in both space x and time t is the superposition of two waves of almost the same wavelength and frequency: [2]
Graph of a sine wave's voltage vs. time (in degrees), showing RMS, peak (PK), and peak-to-peak (PP) voltages. If the waveform is a pure sine wave, the relationships between amplitudes (peak-to-peak, peak) and RMS are fixed and known, as they are for any continuous periodic wave. However, this is not true for an arbitrary waveform, which may not ...
The input sinusoidal voltage is usually defined to have zero phase, meaning that it is arbitrarily chosen as a convenient time reference. So the phase difference is attributed to the current function, e.g. sin(2 π ft + φ), whose orthogonal components are sin(2 π ft) cos(φ) and sin(2 π ft + π /2) sin(φ), as we have seen.