In a sine wave graph, the peak value refers to the maximum positive amplitude reached by the wave, while the valley value represents the minimum negative amplitude reached by the wave. These values can also be referred to as the maximum and minimum values of the wave, respectively.
In mathematical terms, the peak value is equal to the amplitude of the wave, denoted as "A," which represents the distance from the center line (or equilibrium position) to the peak of the wave. The valley value is the negative of the amplitude, denoted as "-A."
The equation for a general sine wave is given by:
y = A * sin(ωt + φ)
where: y represents the instantaneous value of the wave at a given time "t", A is the amplitude or peak value of the wave, ω (omega) is the angular frequency of the wave, t represents time, and φ (phi) is the phase angle.
The peak value of the wave is +A, and the valley value is -A. These values determine the maximum and minimum displacement of the wave from its equilibrium position.