A Level Maths Notes: C3 – Finding Multiple Solutions of Trigonometric Equations
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 – 360o 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
