Inverse Trigonometric Functions and Domain Restrictions

The video tutorial explains the concept of inverse functions for sine, cosine, and tangent. It highlights the necessity of restricting the domain of these functions to make them one-to-one, allowing for the determination of their inverses. The video illustrates the reflection of functions across the line y = x and demonstrates how domain restriction enables the inverse to pass the vertical line test, thus becoming a function. The tutorial covers the sine, cosine, and tangent functions individually, showing the specific domain restrictions required for each to have an inverse.

What is necessary for a function to have an inverse?

• It must be periodic.

• It must be one-to-one.

• It must be differentiable.

• It must be continuous.

Why is the sine function not one-to-one over its entire domain?

• It has multiple y-values for a single x-value.

• A horizontal line intersects it at multiple points.

• It is not differentiable.

• It is not continuous.

What is the restricted domain for the sine function to have an inverse?

• 0 to 2π

• 0 to π

• -π to π

• -π/2 to π/2

What happens to the inverse of the sine function when its domain is restricted?

• It becomes non-differentiable.

• It becomes a periodic function.

• It becomes a one-to-one function.

• It becomes a valid inverse function.

What is the restricted domain for the cosine function to have an inverse?

• 0 to 2π

• -π to π

• -π/2 to π/2

• 0 to π

Why does the cosine function need its domain restricted?

• To make it continuous.

• To make it differentiable.

• To make it periodic.

• To make it one-to-one.

What is the restricted domain for the tangent function to have an inverse?

• 0 to π

• -π/2 to π/2

• -π to π

• 0 to 2π

Why is the tangent function not one-to-one over its entire domain?

• It is periodic.

• It is not differentiable.

• It has vertical asymptotes.

• It is not continuous.

What is the result of restricting the domain of the tangent function?

• It becomes non-differentiable.

• It becomes continuous.

• It becomes a valid inverse function.

• It becomes a periodic function.

Why is domain restriction necessary for inverse trigonometric functions?

• To make them differentiable.

• To ensure they are one-to-one.

• To make them periodic.

• To make them continuous.