The equation that represents the <em>sinusoidal</em> function is
,
.
<h3>Procedure - Determination of an appropriate function based on given information</h3>
In this question we must find an appropriate model for a <em>periodic</em> function based on the information from statement. <em>Sinusoidal</em> functions are the most typical functions which intersects a midline (
) and has both a maximum (
) and a minimum (
).
Sinusoidal functions have in most cases the following form:
(1)
Where:
- Angular frequency
- Angular phase, in radians.
If we know that
,
,
,
and
, then the sinusoidal function is:
(2)
(3)
The resulting system is:
(2b)
(3b)
By applying <em>inverse trigonometric </em>functions we have that:
,
(2c)
,
(3c)
And we proceed to solve this system:


,

By (2c):



The equation that represents the <em>sinusoidal</em> function is
,
. 
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