1. Inverses of Trigonometric Functions

2. The Sine Function Graph Domain: Range: All Reals -1≤y≤1 The Sine graph is a function (one output for each input). Let’s find the inverse of this graph.

3. The Inverse Sine RELATION Graph Domain: Range: -1≤y≤1 All Reals The Inverse Sine graph is NOT a function (multiple outputs for each input). If the range of this graph is restricted, it will become a function. This red portion is a function. The red portion will be known as the inverse sine FUNCTION.

4. The Inverse Sine FUNCTION Graph Domain: Range: -1≤y≤1 With the restriction on the range, the inverse sine function has one output for each input. Every output of the inverse sine function above is known as a principal value of the inverse of sine.

5. The Cosine Function Graph Domain: Range: All Reals -1≤y≤1 The Cosine graph is a function (one output for each input). Let’s find the inverse of this graph.

6. The Inverse Cosine RELATION Graph Domain: Range: -1≤y≤1 All Reals The Inverse Cosine graph is NOT a function (multiple outputs for each input). If the range of this graph is restricted, it will become a function. This red portion is a function. The red portion will be known as the inverse cosine FUNCTION.

7. The Inverse Cosine FUNCTION Graph Domain: Range: -1≤y≤1 With the restriction on the range, the inverse cosine function has one output for each input. Every output of the inverse cosine function above is known as a principal value of the inverse of cosine.

8. The Tangent Function Graph Domain: Range: All Reals The Tangent graph is a function (one output for each input). Let’s find the inverse of this graph.

9. The Inverse Tangent RELATION Graph Domain: Range: All Reals The Inverse Tangent graph is NOT a function (multiple outputs for each input). If the range of this graph is restricted, it will become a function. This red portion is a function. The red portion will be known as the inverse tangent FUNCTION.

10. The Inverse Tangent FUNCTION Graph Domain: Range: All Reals With the restriction on the range, the inverse cosine function has one output for each input. Every output of the inverse tangent function above is known as a principal value of the inverse of tangent.