Angles and the Unit Circle

This video tutorial explains how to find corresponding angles in radians for given points on the unit circle, within the interval from zero to two pi radians. It covers the importance of sketching angles in standard position and determining where the terminal side intersects the unit circle. The tutorial provides examples of calculating angles for specific points in different quadrants, converting degrees to radians, and emphasizes the closed interval on zero radians and open on two pi radians. The video concludes with a discussion on special points and the use of zero radians as the angle.

What is the interval used for finding angles in radians on the unit circle?

• Closed on both 0 and 2π radians

• Open on 0 radians and closed on 2π radians

• Closed on 0 radians and open on 2π radians

• Open on both 0 and 2π radians

What is the angle in radians for the point (0, 1) on the unit circle?

• 3π/2 radians

• π/2 radians

• π radians

• 2π radians

In which quadrant is the point (-√2/2, √2/2) located?

• Fourth quadrant

• First quadrant

• Third quadrant

• Second quadrant

What is the angle in radians for the point (√3/2, -1/2) on the unit circle?

• π/3 radians

• 5π/6 radians

• 7π/6 radians

• 11π/6 radians

Which quadrant contains the point (-1/2, -√3/2)?

• Second quadrant

• Fourth quadrant

• Third quadrant

• First quadrant

What is the angle in radians for the point (√2/2, √2/2) on the unit circle?

• π radians

• 3π/4 radians

• π/2 radians

• π/4 radians

What is the angle in degrees for the point (-1/2, -√3/2)?

• 150 degrees

• 240 degrees

• 210 degrees

• 120 degrees

What is the angle in radians for the point (1, 0) on the unit circle?

• 0 radians

• π radians

• 2π radians

• π/2 radians

Why is 0 radians used instead of 2π radians for the point (1, 0)?

• Because 2π radians is not in the interval

• Because 0 radians is easier to calculate

• Because 0 radians is a full rotation

• Because 2π radians is a negative angle

What is the angle in radians for a complete counterclockwise rotation?

• π/2 radians

• 3π/2 radians

• 2π radians

• π radians