Precalculus : Evaluate Expressions That Include the Inverse Tangent, Cosecant, Secant, or Cotangent 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 Tangent, Cosecant, Secant, Or Cotangent Function

Approximate:  

Possible Answers:

Correct answer:

Explanation:

:

There is a restriction for the range of the inverse tangent function from .

The inverse tangent of a value asks for the angle where the coordinate  lies on the unit circle under the condition that .  For this to be valid on the unit circle, the  must be very close to 1, with an  value also very close to zero, but cannot equal to zero since  would be undefined.  

The point  is located on the unit circle when  , but  is invalid due to the existent asymptote at this angle.

An example of a point very close to  that will yield  can be written as:

Therefore, the approximated rounded value of  is .

Example Question #33 : Graphs And Inverses Of Trigonometric Functions

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

To determine the value of , solve each of the terms first.

The inverse cosine has a domain and range restriction.

The domain exists from , and the range from .  The inverse cosine asks for the angle when the x-value of the existing coordinate is .  The only possibility is  since the coordinate can only exist in the first quadrant.

The inverse sine also has a domain and range restriction.

The domain exists from , and the range from .  The inverse sine asks for the angle when the y-value of the existing coordinate is .  The only possibility is  since the coordinate can only exist in the first quadrant.

Therefore:

Example Question #2 : Evaluate Expressions That Include The Inverse Tangent, Cosecant, Secant, Or Cotangent Function

Determine the correct value of  in degrees.

Possible Answers:

Correct answer:

Explanation:

Rewrite and evaluate .

The inverse sine of one-half is  since  is the y-value of the coordinate when the angle is .

To convert from radians to degrees, replace  with 180.

 

Example Question #1057 : Pre Calculus

Evaluate the following:

Possible Answers:

Correct answer:

Explanation:

For this particular problem we need to recall that the inverse cosine cancels out the cosine therefore,

.

So the expression just becomes 

From here, recall the unit circle for specific angles such as .

Thus,

.

Learning Tools by Varsity Tutors

Incompatible Browser

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