Precalculus : Evaluate Expressions That Include the Inverse Sine or Cosine Function

Study concepts, example questions & explanations for Precalculus

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : Evaluate Expressions That Include The Inverse Sine Or Cosine Function

Find angle A of the following triangle:

Using_inverse_sin_to_find_angle_of_triangle

Possible Answers:

None of the other answers

Correct answer:

Explanation:

We are given the hypotenuse and the side opposite of the angle in question. The trig function that relates these two sides is SIN. Therefore, we can write:

In order to solve for A, we need to take the inverse sin of both sides:

which becomes

Example Question #1 : Evaluate Expressions That Include The Inverse Sine Or Cosine Function

Consider  , where theta is valid from .  What is a possible value of theta?

Possible Answers:

Correct answer:

Explanation:

Solve for theta by taking the inverse sine of both sides.

Since this angle is not valid for the given interval of theta, add  radians to this angle to get a valid answer in the interval.

 

 

Example Question #3 : Evaluate Expressions That Include The Inverse Sine Or Cosine Function

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

First evaluate .

To evaluate inverse cosine, it is necessary to know the domain and range of inverse cosine. 

For: 

The domain  is only valid from .

 is only valid from .

The part is asking for the angle where the x-value of the coordinate is .  The only possibility on the unit circle is the second quadrant.  

Next, evaluate .

Using the same domain and range restrictions, the only valid angle for the given x-value is in the first quadrant on the unit circle.  

Therefore:

Example Question #4 : Evaluate Expressions That Include The Inverse Sine Or Cosine Function

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

To find the correct value of , it is necessary to know the domain and range of inverse cosine.

Domain:  

Range:  

The question is asking for the specific angle when the x-coordinate is half.  

The only possibility is located in the first quadrant, and the point of the special angle is 

The special angle for this coordinate is .

 

Example Question #5 : Evaluate Expressions That Include The Inverse Sine Or Cosine Function

Find the value of .

Possible Answers:

Correct answer:

Explanation:

In order to determine the value or values of , it is necessary to know the domain and range of the inverse sine function.

Domain:  

Range:  

The question is asking for the angle value of theta where the x-value is  under the range restriction.  Since  is located in the first and fourth quadrants, the range restriction makes theta only allowable from .  Therefore, the theta value must only be in the first quadrant.

The value of the angle when the x-value is  is  degrees.

Example Question #6 : Evaluate Expressions That Include The Inverse Sine Or Cosine Function

Find the inverse of the function 

Make sure the final notation is only in the forms including , and 

Possible Answers:

Correct answer:

Explanation:

The easiest way to solve this problem is to simplify the original expression. 

To find its inverse, let's exchange  and 

Solving for 

Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: