Then we have:

Note that the change of variable is not valid if . In that case it will be preferable to define and to transform the initial into an equation in . Then the change of variable may be applied.

Using the above relation any trigonometric equation can be transformed into a polynomial equation which is analyzed using the tools of chapter 5.

It remains to define an interval for angles that we will denote
an *angle interval*.
The element of an angle interval is usually defined between 0 and
(although in most of the following procedures any value can be
used when not specified: internally the element of the angle
interval are converted into value within this range). A difference
between numbers interval (`INTERVAL`) and angle interval is that
the lower bound of an angle interval may be larger than the upper bound.
Indeed the order in an angle interval is
important: for example the angle intervals [0,] and [,0]
are not the same.