Inverse Trigonometric Functions and Their Properties

This video tutorial covers the evaluation of inverse trigonometric expressions, focusing on expressing answers in radians. It explains the importance of understanding the output intervals for inverse sine, cosine, cosecant, and cotangent functions. The tutorial uses reference triangles to evaluate these expressions, providing examples for each function. It also highlights the significance of quadrant placement and textbook definitions in determining the correct angles.

What is the importance of knowing the output interval when evaluating inverse trigonometric expressions?

• It helps in determining the correct angle.

• It is not important at all.

• It helps in simplifying the expression.

• It is only important for sine functions.

Which interval is used for the output of the inverse sine function?

• 0 to π

• -π/2 to π/2

• -π to π

• 0 to 2π

For which function is the output interval from 0 to π, excluding π/2?

• Inverse secant

• Inverse tangent

• Inverse cosine

• Inverse sine

What are the side lengths of a 30/60/90 reference triangle?

• 1, 1, √2

• 1, 2, √3

• 1, √3, 2

• 1, 1, 2

In which quadrant would a 60-degree reference angle with a negative sine value be located?

• First quadrant

• Third quadrant

• Fourth quadrant

• Second quadrant

What is the angle in radians for an inverse sine of negative √3/2?

• -π/3

• -π/6

• π/6

• π/3

What is the reciprocal of a cosecant function value of 2?

• 1/2

• 2

• 1

• 1/3

Which angle has a cotangent function value of -1 in the second quadrant?

• 135 degrees

• 315 degrees

• 45 degrees

• 225 degrees

If a textbook defines the range for inverse cotangent as -π/2 to π/2, what would be the angle for a cotangent value of -1?

• -3π/4

• π/4

• -π/4

• 3π/4

Why is it important to check the textbook definition for the range of inverse cotangent?

• To ensure the correct angle is used.

• To find the exact value of the function.

• To simplify calculations.

• To avoid using reference triangles.