1. Quick Review
Graph the function:
2tan 𝑥+ 𝜋

2. Inverse Trigonometric Functions
Keeper 16
Accelerated Pre-Calculus

3. Inverse Sine Function
The graphs of an equation and its inverse are reflections of each other across the line y = x.
However, the inverse is not a function as it is drawn.

4. Inverse Sine Function
We must restrict the domain of the inverse sine function.
It is fairly standard to restrict it as shown here.
The domain is [–1, 1].
The range is [–π/2, π/2].

5. Inverse Cosine Function
The graphs of an equation and its inverse are reflections of each other across the line y = x.
However, the inverse is not a function as it is drawn.

6. Inverse Cosine Function
We must restrict the domain of the inverse cosine function.
It is fairly standard to restrict it as shown here.
The domain is [–1, 1].
The range is [0, π].

7. Inverse Tangent Function
The graphs of an equation and its inverse are reflections of each other across the line y = x.
However, the inverse is not a function as it is drawn.

8. Inverse Sine Function
We must restrict the domain of the inverse tangent function.
It is fairly standard to restrict it as shown here.
The domain is (–∞, ∞).
The range is (–π/2, π/2).

9. Summary of Inverse Trigonometric Functions
Function Domain Range

10. Examples
Find each of the following function values.

11. More Examples
Find each of the following function values.

12. Composition of Trigonometric Functions
for all x in the domain of sin–1
for all x in the domain of cos–1
for all x in the domain of tan–1

13. Examples

14. Special Cases for all x in the range of sin–1
for all x in the range of cos–1
for all x in the range of tan–1

15. Examples

16. Example
Find