Quick Review Graph the function: 2tan 𝑥+ 𝜋 4 +1

Inverse Trigonometric Functions Keeper 16 Accelerated Pre-Calculus

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.

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].

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.

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].

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.

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).

Summary of Inverse Trigonometric Functions Function Domain Range

Examples Find each of the following function values.

More Examples Find each of the following function values.

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

Examples

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

Examples

Example Find