What is the definition of the inverse cosine function

The video tutorial explains the inverse cosine function, starting with its definition and algebraic approach. It then explores the graphical representation by reflecting the cosine graph over the XY line and swapping coordinates. Key points on the graph are identified, and the importance of domain and range restrictions is discussed to ensure the inverse cosine remains a function.

What is the condition for y to be the inverse cosine of x?

• y is the inverse cosine of x if and only if the secant of y equals x.

• y is the inverse cosine of x if and only if the cosine of y equals x.

• y is the inverse cosine of x if and only if the tangent of y equals x.

• y is the inverse cosine of x if and only if the sine of y equals x.

How is the inverse cosine graph derived from the cosine graph?

• By reflecting the cosine graph over the XY line and swapping coordinates.

• By translating the cosine graph upwards.

• By rotating the cosine graph 90 degrees.

• By reflecting the cosine graph over the Y-axis.

Which of the following is a critical point on the inverse cosine graph?

• (π/2, 1)

• (1, 0)

• (0, π)

• (π, 1)

What is the domain of the inverse cosine function?

• 0 to 1

• 0 to π

• -1 to 1

• -π to π

What is the range of the inverse cosine function?

• 0 to π

• -π to π

• 0 to 1

• -1 to 1