Understanding Inverse Trigonometric Functions Using the Unit Circle

What is the range of angles for the sine inverse function on the unit circle?

• 0 to 2π

• -π to π

• -π/2 to π/2

• 0 to π

Why is the horizontal line test important for inverse trigonometric functions?

• It verifies the function's domain.

• It ensures the inverse is a function.

• It checks if a function is differentiable.

• It determines if a function is continuous.

What is the cosine inverse of -1 on the unit circle?

• -π/2

• π

• 0

• π/2

How do you find the sine inverse of -√3/2 using the unit circle?

• Identify the angle where the tangent is -√3/2

• Find the angle where the y-coordinate is -√3/2

• Locate the angle where the cosine is -√3/2

• Look for the x-coordinate of -√3/2

What is the tangent inverse of 0 on the unit circle?

• -π/2

• π/2

• 0

• π

Which angle corresponds to the arc cosine of -√3/2?

• π/3

• 2π/3

• 5π/6

• π/6

What is the arc sine of 1/2?

• π/6

• π/4

• π/3

• π/2

How do you determine the tangent inverse of √3?

• Look for the angle where the cosine is √3

• Identify the angle where the sine is √3

• Locate the angle where y/x equals √3

• Find where the x-coordinate is √3

What is the sine inverse of -√2/2?

• π/6

• -π/6

• -π/4

• π/4

Which angle is associated with the tangent inverse of 1?

• π/2

• π/3

• π/4

• π/6