Graph of Inverse Functions

The video tutorial covers the inverse trigonometric functions: sine, cosine, cosecant, secant, tangent, and cotangent. It explains their domains, ranges, and how to find their inverses by restricting domains. The concept of principal value branches is introduced, highlighting the unique intervals where these functions are one-to-one and onto. Graphical representations and examples are provided to illustrate these concepts.

What is the principal value branch for the sine inverse function?

• Open interval (-π/2, π/2)

• Closed interval [-π/2, π/2]

• Closed interval [0, π]

• Open interval (0, π)

Which of the following is true about the cosine inverse function?

• Its domain is the set of all real numbers.

• Its range is the open interval (0, π).

• Its principal value branch is the closed interval [0, π].

• It is a one-to-one function over its entire domain.

What is the domain of the cosecant inverse function?

• All real numbers except integral multiples of π

• Real numbers excluding the open interval (-1, 1)

• Closed interval [-1, 1]

• Open interval (0, π)

For the secant inverse function, what is the principal value branch?

• Open interval (0, π)

• Closed interval [0, π] excluding π/2

• Closed interval [-π/2, π/2]

• Open interval (-π/2, π/2)

What is the range of the tangent inverse function's principal value branch?

• Open interval (-π/2, π/2)

• Closed interval [0, π]

• Open interval (0, π)

• Closed interval [-π/2, π/2]

Which interval is the principal value branch for the cotangent inverse function?

• Closed interval [0, π]

• Open interval (0, π)

• Open interval (-π/2, π/2)

• Closed interval [-π/2, π/2]

What is the principal value of sin⁻¹(√3/2)?

• π/6

• π/2

• π/3

• π/4

If cot⁻¹(-√3) = y, what is the principal value of y?

• 2π/3

• 5π/6

• π/2

• π/3

Which of the following is NOT true about inverse trigonometric functions?

• Cosecant inverse excludes the interval (-1, 1) from its domain.

• Sine inverse is the same as 1/sine.

• Cosine inverse has a principal value branch.

• Tangent inverse is defined for all real numbers.

What is the principal value of tan⁻¹(1)?

• π/4

• π/3

• π/6

• π/2