Lesson Six: Inverse Trigonometric Functions

Key Concepts

 Function

 Domain

 Range

 y = arcsin x if and only if sin y = x

 -1 < x < 1

 

 y = arccos x if and only if cos y = x

 -1 < x < 1

 

 y = arctan x if and only if tan y = x

 

 

Graphs of Inverse Trigonometric Functions

 

 

Click here for a GSP file containing the above graphs. Use the tabs at the bottom to toggle between graphs.

Note: These graphs confirm the domains and ranges given above for the inverse trigonometric functions.

Evaluating Inverse Trigonometric Functions Exactly

You can calculate the exact value for some inverse trigonometric functions. The secret to these problems is recognizing the trigonometric values of the special angles: 30, 45, and 60 degrees. Here are some examples.

Approximating Inverse Trigonometric Functions

You can use a calculator to approximate inverse trigonometric functions. For example...

You can also approximate inverse trigonometric functions graphically (similar to the demonstration in lesson 3).

Click here for some interactive practice with sine.

Click here for some interactive practice with cosine.

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