Section 8.3: Inverse Trigonometric Functions Video Quiz

Why do the inverse sine and inverse cosine functions have different ranges?

• Because they are not continuous functions.

• Because they need to be one-to-one functions.

• Because they have different periods.

• Because they are defined on different domains.

What does the equation π/6 = arcsin(0.5) imply?

• sin(π/6) = 0.5

• tan(π/6) = 0.5

• cos(π/6) = 0.5

• arccos(π/6) = 0.5

Why must the domain of the sine function be restricted to [-π/2, π/2] for its inverse to exist?

• To make the function differentiable.

• To make the function periodic.

• To make the function one-to-one.

• To make the function continuous.

What is the value of arccos(-1/2)?

• π/6

• 2π/3

• π/3

• 5π/6

Using a calculator, what is the value of arccos(3/5) rounded to the nearest hundredth?

• 0.93

• 1.41

• 0.67

• 1.23

What is the cosine of arcsin(1/x)?

• √(x^2 - 1)/x

• 1/√(x^2 - 1)

• x/√(x^2 - 1)

• √(x^2 + 1)/x

In a right triangle, if tan(θ) = 12/5, what is cos(θ)?

• 5/13

• 12/13

• 5/12

• 13/5

What is the angle in radians that a 13-foot ladder makes with a building if it reaches a window 12 feet above the ground?

• 0.39

• 0.56

• 1.11

• 0.93

What is the measure of the acute angle adjacent to the 4-foot side in a right triangle with a base of 12 feet and height of 4 feet?

• 1.25 radians

• 0.93 radians

• 0.67 radians

• 1.41 radians

Does a 20-foot ladder placed 10 feet from the base of a building satisfy the safety specifications if the angle of elevation must be between 35 and 45 degrees?

• Yes, because the angle is 35 degrees.

• Yes, because the angle is 40 degrees.

• No, because the angle is 60 degrees.

• No, because the angle is 45 degrees.