Again, Mathcad will only give answers that lie in the
range of the inverse sine function, i. e.,
Take sin(2x) as a common factor
as a common factor
Use the zero product property
To find the other angle (in Quadrant IV) whose cosine
is 1/3, we subtract 70.5 from 360:
Given that cos-1
, solve for x in the interval
(Which property did we use?)
If we substitute x = 180o
in the original equation, we get
. Similarly for the value
x = 270o.
Thus, x = 180o
and x = 270o
are not solutions.
However, because we squared both sides in the process
of the solution, one has to be careful about introducing
"extraneous" solutions (solutions that will
not satisfy the original equation).
Use zero product property
Answer all questions. Show all your work
Solve the following problems for x:
Use the identity
Using the fact that the sine function is odd
The sine function is negative in Quadrant III and IV.
Using the method of the unit circle (see Lecture Notes
web page), we have
Mathcad returned only one value because it used the
inverse sine function (sin-1
). Recall that the range of sin-1
(x) is between
Group to take common factors
Mathcad can be used to check your answer using the "solve"
command as follows:
The solution is given in radians which is the same as
the one we obtained in degrees.