CHAPTER 1 - Fundamentals of Electrical Circuits
20
Euler equation (1.5-4) may also be manipulated to give expressions for both sine and cosine
in terms of complex exponentials
8
as shown in (1.5-11).
( )
( )
Let us use these results to find the derivative of the cosine function. From (1.5-11)(a), we get
( )
( )
( )
[
( ) ( )
]
(
)
This result ties in very well with the results obtained for the derivative of sinusoidal functions
illustrated in section 1.5.2, page 15.
What is also worth pointing out at this stage is that any arbitrary phase shift may be
introduced by using the respective complex exponential
as a multiplicative factor, as shown
below
( )
A
(or
⁄
) phase shift is just a special case of (1.5-12) which takes advantage of (1.5-8).
( )
8
For further insight into this formulae please refer to section 1.5.4.2.
(1.5-12)
(1.5-11)
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