Inverse Trigonometric Functions and Their Properties

This video tutorial explains how to evaluate inverse trigonometric expressions involving inverse cosecant, secant, and cotangent using the unit circle. It covers the range restrictions for each function and demonstrates how to find angles with specific trigonometric values. The video provides examples for each inverse function, showing how to use the unit circle to determine the correct angle in radians or degrees.

What is the range of the inverse cosecant function?

• From -π/2 to π/2, excluding 0

• From 0 to π, excluding π/2

• From -π to π, excluding 0

• From 0 to 2π, excluding π

Which angle corresponds to an inverse cosecant value of -√2?

• -π/4 radians

• π/2 radians

• -π/2 radians

• π/4 radians

What is the reciprocal of the sine function?

• Cosecant

• Tangent

• Secant

• Cotangent

What is the range of the inverse secant function?

• From -π to π, excluding 0

• From 0 to 2π, excluding π

• From -π/2 to π/2, excluding 0

• From 0 to π, excluding π/2

Which angle corresponds to an inverse secant value of -2?

• π/3 radians

• π/6 radians

• 5π/6 radians

• 2π/3 radians

In which quadrant do we find the angle for an inverse secant value of -2?

• Fourth quadrant

• Third quadrant

• First quadrant

• Second quadrant

What is the range of the inverse cotangent function according to most textbooks?

• From 0 to π

• From -π/2 to π/2

• From 0 to 2π

• From -π to π

Which angle corresponds to an inverse cotangent value of √3?

• π/4 radians

• π/2 radians

• π/6 radians

• π/3 radians

What is the relationship between cotangent and the coordinates on the unit circle?

• X divided by Y

• Y divided by X

• X multiplied by Y

• Y multiplied by X

What is the angle in radians for an inverse cotangent value of √3?

• π/6

• π/3

• π/4

• π/2