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.

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CCSS.HSF-BF.B.4D

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.

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CCSS.HSF-BF.B.4D

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

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CCSS.HSF-BF.B.4D

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.

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CCSS.HSF-BF.B.4D

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

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CCSS.HSF-BF.B.4D

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.

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CCSS.HSF-BF.B.4D

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

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CCSS.HSF-BF.B.4D

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.

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CCSS.HSF-BF.B.4D

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.

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CCSS.HSF-BF.B.4D

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.

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CCSS.HSF-BF.B.4D