Inverse Trig Derivative-2011

Name: __________________________________________

A.P. Calculus 1

Inverse Trig. & Derivatives



Overview of the Inverse Trig. Functions

Complete the table.



Inverse Trig. Function & Its Domain Range Evaluate

Graph

sin 1 (1) =



 1 

sin 1   

 2 



 3

sin 1 

 2 



 



cos 1 ( x ) cos 1 (1) =



 1 

cos 1   

 2 



 3

cos 1 

 2 



 



tan 1 (1) =



tan 1 (1) =



tan 1 ( 3) 

cot 1 ( x) cot 1 (1) 



cot 1 ( 3) 



 3

cot 1 

 3 



 





sec 1 (2) 



sec1 (2) 



2 3

sec1 

 3 



 









csc1 ( x) csc 1 (2) 



csc1 (2) 



2 3

csc1 

 3 



 







Derivative of the Inverse Trig. Functions



Please watch the video on the derivative of Inverse Sine. You can find the link to the video on my

webpage https://sites.google.com/site/apcalculus1duty/. As you view the video, answer the following

questions.

1. The Derivative of y  sin 1 ( x).



a. Rewrite the function.





1

b. Take the derivative, implicitly and solve for y  . x

y

c. Rewrite y  in terms of just x.

d  sin 1 (3x 2 ) 

d. Using the derivative for y  sin 1 ( x), find .

dx









Stop the video.



Now it’s your turn!



Answer each of the following.





d cos 1 ( x)

1. Find .

dx









d cos 1 ( x)

=

dx

d tan 1 x

2. Find .

dx









d tan 1 x =

dx









d sec 1 x

3. Find

dx









d sec 1 x

=

dx







Why do you think that the formula for the derivative of sec1 ( x) has an absolute value around the x?

Practice Problems: Find the derivative of each of the following.