How do I get sinusoidal functions into the “standard” form?
When confronted with a sinusoidal function, it is helpful to have it (or get it into) the form
f
(
x
) =
A
sin
p
2
π
B
(
x

C
)
P
+
D
since we are able to read off the parameters A, B, C, and D; these parameters determine
the shape and location of the graph of function. We are always able to put sinusoidal
functions into this form with
A >
0
, and
B >
0
.
Frequently, sinusoidal functions do not appear to us in this form, but we can rewrite in
that form. The following are three examples of how this goes.
1.
f
(
x
) = sin(3
x
+ 1)
We factor out the 3 from the expression
3
x
+ 1
to get
f
(
x
) = sin
p
3
p
x
+
1
3
PP
.
We want
2
π
B
= 3
, so
B
=
2
3
π
. Thus,
f
(
x
) = sin
±
2
π
2
3
π
p
x
+
1
3
P
²
.
And we can see that
A
= 1
,B
=
2
3
π,C
=

1
3
,D
= 0
.
2.
f
(
x
) = sin(2

7
x
)
We can factor the
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 Summer '13
 Dr.MatthewM.Conroy
 Calculus, Sin, Englishlanguage films, Graph of a function, Sine wave, Identity element

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