Inverse Trigonometric Functions and Their Properties

The video tutorial explains how to evaluate an inverse trigonometric expression, specifically the inverse cosecant of -2√3/3, in both degrees and radians. It highlights the importance of understanding the range of the inverse cosecant function, which is from -π/2 to π/2 in radians or -90 to 90 degrees. The tutorial demonstrates the reciprocal relationship between cosecant and sine functions, rationalizes the sine function value, and uses reference triangles and quadrants to determine the angle θ, which is -60 degrees or -π/3 radians.

What is the primary goal when evaluating an inverse trigonometric expression?

• To determine the area of a triangle

• To calculate the length of the hypotenuse

• To convert degrees to radians

• To find the angle that corresponds to a given trigonometric value

Why is it important to know the range of the inverse cosecant function?

• To find the length of the opposite side

• To convert radians to degrees

• To calculate the sine value

• To determine the correct angle within a specific interval

What is the relationship between cosecant and sine functions?

• They are inverses of each other

• They are equal to each other

• They are reciprocals of each other

• They are unrelated

How do you find the sine value from a given cosecant value?

• By taking the reciprocal of the cosecant value

• By multiplying the cosecant value by 2

• By subtracting 1 from the cosecant value

• By adding 1 to the cosecant value

What is the sine function value for a 60-degree angle in a 30-60-90 triangle?

• Square root of 3 over 2

• 1

• Square root of 2 over 2

• 1 over 2

What is the reference angle for a sine value of -square root of 3 over 2?

• 45 degrees

• 90 degrees

• 30 degrees

• 60 degrees

In which quadrant is the reference angle located for a negative sine value?

• Fourth quadrant

• First quadrant

• Second quadrant

• Third quadrant

What is the angle in degrees for the inverse cosecant of -2 square root 3 divided by 3?

• 30 degrees

• -30 degrees

• 60 degrees

• -60 degrees

What is the angle in radians for the inverse cosecant of -2 square root 3 divided by 3?

• -pi/3 radians

• pi/3 radians

• -pi/6 radians

• pi/6 radians

What is the significance of the coordinate plane in evaluating inverse trigonometric expressions?

• It is used to calculate the hypotenuse

• It helps determine the correct quadrant for the angle

• It converts degrees to radians

• It is used to find the area of a triangle