Review : Solving Trig Equations with Calculators, Part II
Because this document is also being prepared for viewing on
the web we split this section into two parts to keep the size of the pages to a
minimum.
Also, as with the last few examples in the previous part of
this section we are not going to be looking for solutions in an interval in
order to save space. The important part of these examples is to find the
solutions to the equation. If we�d been given an interval it would be easy
enough to find the solutions that actually fall in the interval.
In all the examples in the previous section all the
arguments, the
 ,
 ,
etc., were fairly simple. Let�s take a look at an example that has a
slightly more complicated argument.
Example
Solve
 .
Solution
Note that the argument here is not really all that
complicated but the addition of the �-1� often seems to confuse people so we
need to a quick example with this kind of argument. The solution process is
identical to all the problems we�ve done to this point so we won�t be putting in
much explanation. Here is the solution.
This angle is in the second quadrant and so we can use
either -2.2143 or
 for
the second angle. As usual for these notes we�ll use the positive one.
Therefore the two angles are,
Now, we still need to find the actual values of x
that are the solutions. These are found in the same manner as all the problems
above. We�ll first add 1 to both sides and then divide by 2. Doing this gives,
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