Understanding Angles and Trigonometric Functions

The video tutorial explains how to evaluate the inverse trigonometric expression arc secant of -2 in both degrees and radians. It covers the relationship between secant and cosine, using the 30-60-90 triangle to find the reference angle. The tutorial demonstrates how to determine the angle in the second quadrant and convert it to radians. It also shows how to verify the result using a calculator, emphasizing the importance of checking the mode setting.

What is the range of the arc secant function in degrees?

• 0 to 90 degrees

• 0 to 180 degrees

• 0 to 360 degrees

• 90 to 180 degrees

If secant theta is -2, what is cosine theta?

• -2

• 1/2

• -1/2

• 2

Which triangle is useful for identifying angles with a cosine of -1/2?

• Equilateral triangle

• Scalene triangle

• 45-45-90 triangle

• 30-60-90 triangle

In which quadrant is the angle if the cosine value is negative?

• Second quadrant

• First quadrant

• Fourth quadrant

• Third quadrant

What is the angle in degrees if the reference angle is 60 degrees in the second quadrant?

• 60 degrees

• 120 degrees

• 150 degrees

• 180 degrees

How do you convert 120 degrees to radians?

• 3π/2 radians

• π/2 radians

• π/3 radians

• 2π/3 radians

What is the first step to verify the angle using a calculator?

• Use the tangent function

• Use the sine function

• Check the mode is set to degrees

• Check the mode is set to radians

Which function on the calculator helps verify the angle for cosine -1/2?

• Inverse cosine

• Inverse secant

• Inverse tangent

• Inverse sine

What is the result of inverse cosine of -1/2 in degrees?

• 180 degrees

• 60 degrees

• 90 degrees

• 120 degrees

Why is it important to set the calculator to degree mode for this problem?

• To simplify calculations

• To recognize the angle correctly

• To avoid complex numbers

• To get the answer in terms of π