Arc Length and Central Angles

The video tutorial explains the concept of arc length, denoted as 's', and introduces the formula s = Rθ, which relates the radius, central angle, and arc length. It emphasizes that the angle θ must be in radians for the formula to be applicable. An example is provided where a circle with a radius of 10 cm and a central angle of π/4 radians is used to calculate the arc length, resulting in an exact answer of 5π/2 cm.

What is the formula for calculating arc length?

• s = θR²

• s = Rθ

• s = R/θ

• s = θ/R

In the formula s = Rθ, what does 'R' represent?

• Diameter

• Radius

• Central angle

• Arc length

What is the relationship between the radius and the arc length?

• Unrelated

• Inversely proportional

• Exponentially related

• Directly proportional

What happens to the arc length if the radius is doubled?

• It remains the same

• It quadruples

• It halves

• It doubles

What must the central angle be measured in to use the formula s = Rθ?

• Degrees

• Radians

• Gradians

• Revolutions

If a central angle is given in degrees, what should you do before using the formula s = Rθ?

• Convert it to arc minutes

• Convert it to radians

• Convert it to revolutions

• Convert it to gradians

In the example problem, what is the radius of the circle?

• 20 cm

• 10 cm

• 5 cm

• 15 cm

What is the central angle in the example problem?

• π/3 radians

• π/2 radians

• π/6 radians

• π/4 radians

What is the first step in solving the example problem?

• Convert the angle to degrees

• Add the radius and angle

• Identify the radius and angle

• Divide the radius by the angle

How do you calculate the arc length in the example problem?

• Divide the radius by the angle

• Multiply the radius by the angle

• Add the radius and the angle

• Subtract the angle from the radius