Understanding Radians

This video tutorial explains the concept of radians as a unit of angle measure, equivalent to approximately 57.3 degrees. It describes how radians are derived from the relationship between the arc length and the radius of a circle. The video also covers the calculation of radians in a full circle, which is 2π radians or 360 degrees. Additionally, it provides a step-by-step guide on converting between degrees and radians, using examples to illustrate the process.

What is the approximate degree measure of one radian?

• 90 degrees

• 45 degrees

• 57.3 degrees

• 60 degrees

How many degrees are there in a full circle?

• 540 degrees

• 360 degrees

• 270 degrees

• 180 degrees

What is the relationship between the arc length and the radius when the angle is one radian?

• Arc length is three times the radius

• Arc length is twice the radius

• Arc length is equal to the radius

• Arc length is half the radius

If a circle has a radius of 4 inches and an angle measure of 2 radians, what is the arc length?

• 4 inches

• 6 inches

• 8 inches

• 10 inches

How many radians are there in a complete circle?

• π radians

• 2π radians

• 4π radians

• 6π radians

What is the formula to convert degrees to radians?

• Multiply by π/180

• Multiply by 180/π

• Multiply by 360/π

• Multiply by π/360

Convert 30 degrees to radians.

• π/4

• π/2

• π/6

• π/3

Convert 60 degrees to radians.

• π/4

• π/2

• π/6

• π/3

Convert 5π/6 radians to degrees.

• 150 degrees

• 120 degrees

• 180 degrees

• 210 degrees

Convert 4π/3 radians to degrees.

• 180 degrees

• 240 degrees

• 270 degrees

• 210 degrees