All Trigonometry Resources
Example Questions
Example Question #1 : Arcsin, Arccos, Arctan
What is if
and
?
In order to find we need to utilize the given information in the problem. We are given the opposite and adjacent sides. We can then, by definition, find the
of
and its measure in degrees by utilizing the
function.
Now to find the measure of the angle using the function.
If you calculated the angle's measure to be then your calculator was set to radians and needs to be set on degrees.
Example Question #1 : Arcsin, Arccos, Arctan
For the above triangle, what is if
and
?
We need to use a trigonometric function to find . We are given the opposite and adjacent sides, so we can use the
and
functions.
Example Question #1 : Arcsin, Arccos, Arctan
For the above triangle, what is if
and
?
We need to use a trigonometric function to find . We are given the opposite and hypotenuse sides, so we can use the
and
functions.
Example Question #1 : Arcsin, Arccos, Arctan
Which of the following is the degree equivalent of the inverse trigonometric function
?
The is the reversal of the cosine function. That means that if
, then
.
Therefore,
Example Question #5 : Arcsin, Arccos, Arctan
Assuming the angle in degrees, determine the value of .
To evaluate , it is necessary to know the existing domain and range for these inverse functions.
Inverse sine:
Inverse cosine:
Inverse tangent:
Evaluate each term. The final answers must return an angle.
Example Question #1 : Arcsin, Arccos, Arctan
If
,
what value(s) does take?
Assume that
No real solution.
If , then we can apply the cosine inverse to both sides:
Since cosine and cosine inverse undo each other; we can then apply sine and secant inverse functions to obtain the solution.
and
and
are the two solutions.
Example Question #6 : Arcsin, Arccos, Arctan
Calculate .
and
The arcsecant function takes a trigonometric ratio on the unit circle as its input and results in an angle measure as its output. The given function can therefore be rewritten as
and is the angle measure which, when applied to the cosine function
, results in
. Notice that the arcsecant function as expressed in the statement of the problem is capitalized; hence, we are looking for the "principal" angle measure, or the one which lies between
and
. Since
, and since
lies between
and
,
.
Example Question #7 : Arcsin, Arccos, Arctan
Calculate .
The domain on the argument for
is
.
The range of the function is not defined at
or
, and so the domain of its inverse,
, does not include those values. Hence, we must find the angle
between
and
for which
.
Since , the equation
can be rewritten as
,
or
for some x between and
.
Now, when
, since
.
Therefore,
.
All Trigonometry Resources
![Learning Tools by Varsity Tutors](https://vt-vtwa-app-assets.varsitytutors.com/assets/problems/og_image_practice_problems-9cd7cd1b01009043c4576617bc620d0d5f9d58294f59b6d6556fd8365f7440cf.jpg)