Sinusoidal Signal

 A sinusoidal signal as show in the figure can be represented by,

                                                       f(t)=A sinwt ; Where A is peak amplitude and w is angular frequency in radians/second

Sinusoidal signal is a periodic signal with time period T and frequency f which denotes number of cycles of signal that took place in a second.

$w = 2\pi f$ where f is frequency in herzt. The time period $T = \frac{{2\pi }}{w} = \frac{1}{f}$

Higher the frequency smaller the time period.

The angle $\theta$ is called the phase angle of sinusoid.

Consider a sine function, $v(t) = {V_m}\sin \omega t$

Then average value of v(t) =$\frac{{{V_m}}}{T}\int\limits_0^T {\sin \omega tdt = \frac{{{V_m}}}{T}} \mathop {\left[ {\frac{{\cos \omega t}}{\omega }} \right]}\nolimits_0^T  = 0$

Thus, the average value of sine wave is zero.

The rms value of the sine wave is,     ${V_{rms}} = \frac{1}{{2\pi }}\int\limits_0^{2\pi } {\mathop {{V_m}}\nolimits^2 } \mathop {\sin }\nolimits^2 (\omega t)d(\omega t) = \frac{{{V_m}}}{{\sqrt 2 }}$