The differential of the sine function is the cosine function while the differential of the cosine function is the negative of the sine function.
By its very mane, a sinusoidal wave refers to a sine function. The cosine function is simply the sine function that is phase-shifted.
Generating Sine and Cosine Signals (Use updated lab)
Sine(A+ B) = Sine(A)*Cosine(B) + Cosine(A)*Sine(B).
Tangent = sine/cosine provided that cosine is non-zero. When cosine is 0, then tangent is undefined.
Negative cosine f(x) = sin(x) f'(x) = -cos(x)
A simple wave function can be expressed as a trigonometric function of either sine or cosine. lamba = A sine(a+bt) or lamba = A cosine(a+bt) where lamba = the y value of the wave A= magnitude of the wave a= phase angle b= frequency. the derivative of sine is cosine and the derivative of cosine is -sine so the derivative of a sine wave function would be y'=Ab cosine(a+bt) """"""""""""""""""" cosine wave function would be y' =-Ab sine(a+bt)
This question makes no sense as the specified condition cannot occur. The phase shift between a sine wave and a cosine wave is always 90 degrees, by definition.
It's called a sine wave because the waveform can be reproduced as a graph of the sine or cosine functions sin(x) or cos (x).
Should be a sine ( or cosine) wave.
By its very mane, a sinusoidal wave refers to a sine function. The cosine function is simply the sine function that is phase-shifted.
Generating Sine and Cosine Signals (Use updated lab)
Sine(A+ B) = Sine(A)*Cosine(B) + Cosine(A)*Sine(B).
The sinusoidal wave is harmonically pure, i.e. it only has one frequency in the frequency domain. If it were not harmonically pure, i.e. if it were not sinusoidal, it would be more difficult, if not impossible, to demodulate it at the receiver.
Neither wave is smoother than the other. However, the two waves are usually evaluated from 0 to 2*pi, and in that case, the cosine wave begins at y=1, and the sine wave begins at 0.
Sine= Opposite/ Hypotenuse Cosine= Adjacent/ Hypotenuse
Tangent = sine/cosine provided that cosine is non-zero. When cosine is 0, then tangent is undefined.
Negative cosine f(x) = sin(x) f'(x) = -cos(x)