Understanding Radians and Degrees

The video tutorial explains the concept of radians, a unit of angular measure, and its relationship with degrees. It covers the conversion process between radians and degrees, using pi as a conversion factor. The tutorial provides examples of converting degrees to radians and vice versa, emphasizing the cancellation of units and simplification of fractions. It also highlights the importance of recognizing radians and degrees based on symbols and context.

What is a radian?

• An angle that subtends an arc equal to twice the radius

• An angle that subtends an arc equal to half the radius

• An angle that subtends an arc equal to the diameter

• An angle that subtends an arc equal to the radius

How many radians are there in a full circle?

• π radians

• 360 radians

• 2π radians

• 180 radians

What is the conversion factor from degrees to radians?

• π/90

• 180/π

• π/180

• 90/π

Convert 45 degrees to radians.

• π/2 radians

• π/4 radians

• π/3 radians

• π/6 radians

Convert 100 degrees to radians.

• 2π/9 radians

• 5π/9 radians

• 10π/9 radians

• π/9 radians

Convert 2π/9 radians to degrees.

• 60 degrees

• 20 degrees

• 80 degrees

• 40 degrees

Convert 5π/4 radians to degrees.

• 180 degrees

• 90 degrees

• 225 degrees

• 135 degrees

What indicates that an angle is in radians if no symbol is present?

• Absence of a degree symbol

• Presence of a degree symbol

• Presence of a pi symbol

• Absence of a pi symbol

If an angle is written as 3, what unit is it in?

• Radians

• Degrees

• Revolutions

• Gradians

What is the approximate degree measure of one radian?

• 30 degrees

• 90 degrees

• 45 degrees

• 57 degrees