Determining Domain and Range of Inverse Trigonometric Functions

The video tutorial explains how to identify the domain and range of the trigonometric functions sine, cosine, and tangent. It also covers the domain and range of their inverse functions. The instructor uses graphs to illustrate these concepts, emphasizing the importance of understanding the parent graphs and their inverses. The video also discusses the restrictions necessary for inverse functions to remain valid functions, focusing on the need to restrict the range for sine and cosine inverses.

Which trigonometric functions are discussed in the video?

• Sine, Cosine, and Secant

• Sine, Tangent, and Cotangent

• Cosine, Tangent, and Cosecant

• Sine, Cosine, and Tangent

What is the domain of the sine function?

• Negative 1 to 1

• Negative infinity to infinity

• 0 to π

• 0 to 2π

What is the range of the cosine function?

• Negative infinity to infinity

• 0 to 2π

• Negative 1 to 1

• 0 to π

What are the vertical asymptotes in the tangent function?

• π/4 and -π/4

• π and -π

• π/2 and -π/2

• 0 and π

What is the range of the tangent function?

• Negative infinity to infinity

• Negative 1 to 1

• 0 to π

• Negative π/2 to π/2

How do you find the inverse of a function?

• Reflect the graph about the y-axis

• Rotate the graph 90 degrees

• Reflect the graph about the x-axis

• Swap the x and y values

What is the domain of the inverse sine function?

• Negative infinity to infinity

• Negative 1 to 1

• 0 to π

• Negative π/2 to π/2

What is the range of the inverse cosine function?

• Negative π/2 to π/2

• 0 to π

• Negative 1 to 1

• Negative infinity to infinity

What happens if the range of the inverse sine function is not restricted?

• It becomes a linear function

• It becomes a constant function

• It becomes a periodic function

• It no longer remains a function

What is the range of the inverse tangent function?

• Negative π/2 to π/2

• 0 to π

• Negative 1 to 1

• Negative infinity to infinity