Finding Multiple Solutions of Trigonometric Equatioins
In general a trigonometric equation of the form
for example may have more than one solution, and may have in fact an infinite number of solutions. We often have to find the solutions within a certain range eg 0 – 360 o or
depending on whether we are working in degrees or radians. All the trigonometric graphs – sin, cos and tan – possess symmetry.
All the graphs repeat every
This means that if
is a solution to a trigonometric equation, then
will also be a solution for any integer n. However there are also specific rules for each function.
Example:
Solve
Since sin repeats every
and is symmetrical about the lines
are also solutions.
The complete set of solutions is
Solve
Since cos repeats everyand is symmetrical about the lines
are also solutions.
The complete set of solutions is
Solve
Since tan repeats every
and is not symmetrical about any line
are also solutions.
The complete set of solutions is
