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Unformatted text preview: ave already discussed period, that is, how
long it takes for the sinusoid to complete one cycle. The standard period of both f (x) = cos(x) and
g (x) = sin(x) is 2π , but horizontal scalings will change the period of the resulting sinusoid. The
amplitude of the sinusoid is a measure of how ‘tall’ the wave is, as indicated in the ﬁgure below.
The amplitude of the standard cosine and sine functions is 1, but vertical scalings can alter this.
6 We have already seen how the Even/Odd and Cofunction Identities can be used to rewrite g (x) = sin(x) as a
transformed version of f (x) = cos(x), so of course, the reverse is true: f (x) = cos(x) can be written as a transformed
version of g (x) = sin(x). The authors have seen some instances where sinusoids are always converted to cosine
functions while in other disciplines, the sinusoids are always written in terms of sine functions. We will discuss the
applications of sinusoids in greater detail in Chapter 11. Until then, we will keep our options open. 10.5...
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