Understanding Radians and Degrees

The video tutorial explains the concept of radian measure as an alternative to degrees for measuring angles. It covers the relationship between radians, the radius, and arc length, and provides a detailed explanation of how to convert between radians and degrees. The tutorial also addresses negative angles and offers practical examples, such as calculating the movement of a clock's minute hand and a snowboarder's spin. The video concludes with helpful hints for interpreting angle measures.

What is the primary difference between radians and degrees?

• Radians are larger units than degrees.

• Radians are based on the radius and arc length, while degrees are based on a fraction of a circle.

• Radians are used for measuring distances, while degrees measure angles.

• Degrees are used in the metric system, while radians are not.

How is a radian defined in terms of a circle?

• As the angle whose arc length is equal to the radius.

• As the angle formed by a complete circle.

• As the angle whose arc length is twice the radius.

• As the angle formed by a quarter of a circle.

What is the conversion factor from degrees to radians?

• Multiply by 360/pi

• Multiply by pi/180

• Multiply by 180/pi

• Multiply by pi/360

If you have an angle of 30 degrees, what is its equivalent in radians?

• pi/6

• pi/4

• pi/3

• pi/2

How do you convert radians back to degrees?

• Multiply by 180/pi

• Multiply by pi/180

• Multiply by pi/360

• Multiply by 360/pi

What is the degree measure of an angle that is -3pi/4 radians?

• -90 degrees

• -135 degrees

• -45 degrees

• -180 degrees

How many degrees does a clock's minute hand move in one minute?

• 6 degrees

• 10 degrees

• 12 degrees

• 5 degrees

If a snowboarder spins 1.5 rotations, how many degrees has he spun?

• 180 degrees

• 720 degrees

• 540 degrees

• 360 degrees

What is the radian measure of a full circle?

• 4pi radians

• 3pi radians

• 2pi radians

• pi radians

How many radians does a clock's minute hand move in 5 minutes?

• pi/6 radians

• pi/3 radians

• pi/2 radians

• pi radians