### All Trigonometry Resources

## Example Questions

### Example Question #1 : Understanding Arcsine, Arccosine, And Arctangent

What is if and ?

**Possible Answers:**

**Correct answer:**

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 #2 : Arcsin, Arccos, Arctan

For the above triangle, what is if and ?

**Possible Answers:**

**Correct answer:**

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 #3 : Arcsin, Arccos, Arctan

For the above triangle, what is if and ?

**Possible Answers:**

**Correct answer:**

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

?

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

**Correct answer:**

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

**Possible Answers:**

No real solution.

**Correct answer:**

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 #2 : Arcsin, Arccos, Arctan

Calculate .

**Possible Answers:**

and

**Correct answer:**

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 #1 : Arcsin, Arccos, Arctan

Calculate .

**Possible Answers:**

**Correct answer:**

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,

.

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