Sine and Cosine Wave Relationships The sine and cosine are essentially the same function, but with a 90° phase difference. sin ot = cos (ot -90°) Multiples of 360° may be added to or subtracted from the argument of any sinusoidal function without changing the value of the function. To realize this, let us consider the sine wave A, lead Az by 150°. where: A = Api cos (10t +20) = Api sin (10t + 90° + 20) = Api sin (10t + 110") It is also correct to say that A, lags A; by 210°, since Ai may be written as A1 = Api sin (10t -250°) (HOW!) A2 = Ape sin (10t -40)
Sine and Cosine Wave Relationships The sine and cosine are essentially the same function, but with a 90° phase difference. sin ot = cos (ot -90°) Multiples of 360° may be added to or subtracted from the argument of any sinusoidal function without changing the value of the function. To realize this, let us consider the sine wave A, lead Az by 150°. where: A = Api cos (10t +20) = Api sin (10t + 90° + 20) = Api sin (10t + 110") It is also correct to say that A, lags A; by 210°, since Ai may be written as A1 = Api sin (10t -250°) (HOW!) A2 = Ape sin (10t -40)
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Transcribed Image Text:Sine and Cosine Wave Relationships
The sine and cosine are essentially the same function, but with a 90° phase difference.
sin øt = cos (@t -90°)
Multiples of 360° may be added to or subtracted from the argument of any sinusoidal function
without changing the value of the function. To realize this, let us consider the sine wave A,
lead Az by 150°. where:
A = Api cos (10t +20°)
= Api sin (10t + 90° + 20°)
= Api sin (10t + 110)
It is also correct to say that A, lags A2 by 210°, since A may be written as
A: = Ape sin (10t -40°)
Aj = Api sin (10t -250°) (HOW!)
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