Basic
Trigonometric Equations: 
When
asked to solve 2x  1 = 0, we can
easily get 2x = 1 and x =
as the answer.
When
asked to solve 2sinx  1 = 0, we
proceed in a similar manner. We
first look at
sinx as being the
variable of the equation and solve as we
did in the first example.

2sinx
 1 = 0
2sinx
= 1
sinx
=


But, we
are only half way to the answer!!!

If we recall the graph of
, we will
remember that there are actually TWO values of
for which
the = 1/2.
These values are at:
or at 30º and 150º. 
If we look at the
extended graph of
,
we see that there are many other
solutions to this equation
= 1/2.
We could arrive
at these "other" solutions by
adding a multiple of
to
.
. 

Most equations,
however, limit the answers to
trigonometric equations to the domain
.
(Always read the question
carefully to determine the given
domain.)
Solutions
of trigonometric equations may also be
found by examining the sign of the trig
value and determining the proper
quadrant(s) for that value.
Example 1:
Solution:
First, solve for sin x.
Now, sine is
negative in Quadrant III and
Quadrant IV.
Also, a sine
value of
is a reference angle of 45º. So,
consider the reference angle of
45º in quadrants III and IV.


Example 2:
Solution:
First, solve for tan x.
Now, tangent is
negative in Quadrant II and
Quadrant IV.
Also, a tangent
value of
is a reference angle of 60
degrees. So,
consider the reference angle of
60º in quadrants II and IV.



How
to use your
TI83+/84+ graphing
calculator to
solve trigonometric
equations.
Click calculator. 

