Converting Angles: Radians to Degrees

This video tutorial explains how to convert angles from radian measure to degree measure using unit fractions. It begins with the definition that 2π radians equal 360 degrees and introduces unit fractions for conversion. The video provides examples of converting angles with and without π, demonstrating the simplification process and the use of a calculator for non-π angles.

What is the purpose of using a unit fraction in angle conversion?

• To subtract angles

• To simplify the equation

• To change the angle's unit

• To add angles together

What is the relationship between radians and degrees used in unit fractions?

• π radians = 360°

• 2π radians = 180°

• π radians = 180°

• 2π radians = 360°

How do you convert an angle from radians to degrees?

• Divide by π/180

• Multiply by 180/π

• Multiply by π/180

• Divide by 180/π

In the first example, what common factor is used to simplify 6 and 180?

• 3

• 6

• 9

• 12

What is the result of converting 5π/6 radians to degrees?

• 120°

• 150°

• 180°

• 210°

In the second example, what is the common factor between 9 and 180?

• 9

• 6

• 3

• 12

What is the degree measure of -2π/9 radians?

• -20°

• -30°

• -50°

• -40°

How do you handle radian measures without pi during conversion?

• Divide by 180

• Add 180 to the result

• Multiply by π

• Use a calculator for decimal approximation

What is the approximate degree measure of 2.1 radians?

• 150.3°

• 120.3°

• 130.3°

• 140.3°

Why is it uncommon to express angles in degrees with a pi in it?

• Degrees are always whole numbers

• Pi is only used in radians

• It complicates calculations

• It is not a standard practice