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.
cos wave
By shifting the sine wave by 45 degrees.
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).
By its very mane, a sinusoidal wave refers to a sine function. The cosine function is simply the sine function that is phase-shifted.
Negative cosine f(x) = sin(x) f'(x) = -cos(x)
Cos is short for Cosine ( Complementary Sine) Similrly Sin is short for Sine Tan is short for Tangent.
Well sin, cos and tan can all be grouped into the section called sinusoidal functions, dunno if that's what you were looking for.
The Fourier transform of a sine wave is a pair of delta functions located at the positive and negative frequencies of the sine wave.
A sine wave is the graph of y = sin(x). It demonstrates to cyclic nature of the sine function.
The voice is not a sine wave.
a phase shifted sine wave of a different amplitude.
Sine wave is considered as the AC signal because it starts at 0 amplitude and it captures the alternating nature of the signal. Cosine wave is just a phase shift of the sine wave and represents the same signal. So, either sine or cosine wave can be used to represent AC signals. However, sine wave is more conventionally used.