Graphing Calculator Investigations Relating to Inverse Trig Functions Topic Index | Algebra2/Trig Index | Regents Exam Prep Center

These questions are good "class" activities or group activities.
Follow-up discussion is crucial to ensure understanding of the concepts.

Have students show their solutions to the class using the teacher's overhead projection device or TI-SmartView software (if you are using a SmartBoard or a Projection device for your computer).  Texas Instruments also offers a "Presentation Link Adapter" which gives students a means of displaying their own calculator's work on the teacher's ViewScreen.  The adapter connects a student TI-84+ calculator to the TI-Presenter or the overhead ViewScreen, allowing students to quickly display their work to the class.   

Grab your graphing calculator!
 

1.	Determine the domain  and range of sin-1 (x) using the graphing calculator.	The calculator is used to verify the domain and range of the inverse functions.  The TRACE option and the TABLE are used.
2.	For what values of x is cos(cos-1 (x)) = x?	This question leads to an interesting investigation of the composition of a trig function with its inverse.  To examine this situation further, see Composition with Inverse Trig Functions.
3.	Evaluate sin(sin-1(2.1)) in Radian mode.	Why is there no answer?  Why is it not returning the "starting value" as inverse functions do when composed with their original functions?
5.	When working in degrees, is it true that ?	Explain why this is true or not true.
6.	Verify by graphing that sin(sin-1(x)) = x cos(cos-1(x)) = x tan(tan-1(x)) = x sin-1(sin (x)) = x cos-1(cos (x)) = x tan-1(tan (x)) = x are all true when considering the restricted domains for each inverse function.	Assign different statements to different groups or investigate only selected statements.