Exploring Arc Length and Radian Measure

This lesson covers arc length, radian measure, and sector area. It explains how to calculate arc length using the circumference formula and how to convert between degrees and radians. The lesson also demonstrates finding the area of a sector, emphasizing the use of formulas and proportions. Examples are provided to illustrate these concepts, and the lesson concludes with a summary of key points.

What is the formula for calculating arc length?

• s = angle measure / 2π * 360

• s = angle measure / 360 * 2πr

• s = 360 / angle measure * 2πr

• s = angle measure * 360 / 2πr

How can arc length be expressed in terms of proportion?

• Arc length + Circumference = Angle measure / 360

• Arc length * Circumference = Angle measure / 360

• Arc length / Circumference = Angle measure / 360

• Arc length / Circumference = 360 / Angle measure

What is the relationship between the arc length and the circumference of a circle?

• Unrelated

• Directly proportional

• Inversely proportional

• Equal

If the radius of a circle is doubled, how does the arc length change for a fixed central angle?

• It doubles

• It quadruples

• It remains the same

• It halves

What is the equivalent of 360 degrees in radians?

• 2π radians

• π radians

• 360π radians

• 180π radians

How do you convert degrees to radians?

• Multiply by π / 180

• Multiply by 180 / π

• Divide by π / 180

• Divide by 180 / π

How do you convert radians to degrees?

• Multiply by 180 / π

• Multiply by π / 180

• Divide by π / 180

• Divide by 180 / π

What is the result of converting π radians to degrees?

• 90 degrees

• π degrees

• 180 degrees

• 360 degrees

What is the formula for finding the area of a sector?

• Area = (Angle measure / 360) * πr^2

• Area = πr^2 / (Angle measure / 360)

• Area = πr^2 * (Angle measure / 360)

• Area = (Angle measure * 360) / πr^2

If the central angle of a sector is 210 degrees and the radius is 3, what is the area of the sector?

• 16.149 square units

• 5.25π square units

• 21π / 4 square units

• 63π / 12 square units