# Sinusoid

The sinusoid (adjective sinusoidal ) is a sinusoidal function derived from the sine function by scaling of amplitude and frequency and phase shifting is formed. It forms the basis of the representation in the frequency domain .

## definition

The sinusoid is defined by ${\ displaystyle x}$

${\ displaystyle x \ left (t \ right): = A \ sin {\ bigl (} \ omega t + \ varphi {\ bigr)} + ​​C}$,

in which

• ${\ displaystyle A}$the scaling of the amplitude ,
• ${\ displaystyle \ omega}$the scaling of the angular frequency
• ${\ displaystyle \ varphi}$the phase shift and
• ${\ displaystyle C}$ the absolute term

is. In electrical engineering , the absolute term is the constant component over time .

## cosine

Since one function of the form is also a sinusoid, the other trigonometric functions are not. ${\ displaystyle \ cos \ left (t \ right) = \ sin \ left (t + {\ tfrac {\ pi} {2}} \ right)}$${\ displaystyle x \ left (t \ right) = A \ cos \ left (\ omega t + \ varphi \ right) + C}$