Understanding Arc Length and Radians

The video tutorial explains how to find the length of an arc in a circle using radians. It begins by defining the problem and introducing variables such as the central angle, arc length, and radius. The relationship between radians and arc length is discussed, emphasizing that the radian measure is the ratio of the arc length to the radius. The tutorial then demonstrates solving the problem by applying the formula s = rθ, where s is the arc length, r is the radius, and θ is the angle in radians. The solution is calculated to be 9 centimeters.

What is the measure of the central angle GOH in radians?

• 2 radians

• 5/2 radians

• 3/2 radians

• 1/2 radians

What is the radius of the circle given in the problem?

• 7 cm

• 6 cm

• 5 cm

• 4 cm

What does the radian measure of an angle represent?

• The diameter of the circle

• The circumference of the circle

• The ratio of the arc length to the radius

• The degree measure of the angle

How is the arc length related to the central angle in radians?

• Arc length is the sum of the angle in radians and the radius

• Arc length is the difference between the angle in radians and the radius

• Arc length is the product of the angle in radians and the radius

• Arc length is the product of the angle in degrees and the radius

What is the formula for calculating the arc length?

• s = r / theta

• s = r * theta

• s = r - theta

• s = r + theta

What is the length of arc GH when the radius is 6 cm and the angle is 3/2 radians?

• 6 cm

• 9 cm

• 12 cm

• 15 cm

If the radius of a circle is doubled, how does it affect the arc length for the same angle?

• The arc length is halved

• The arc length remains the same

• The arc length is doubled

• The arc length is quadrupled

What happens to the arc length if the angle in radians is halved?

• The arc length is quadrupled

• The arc length is doubled

• The arc length remains the same

• The arc length is halved

Which of the following is true about a unit circle?

• Its radius is 1 unit

• Its circumference is 2π units

• Its radius is 2 units

• Its diameter is 1 unit

What is the relationship between the arc length and the radius in a unit circle?

• Arc length is half the radius

• Arc length equals the radius

• Arc length is twice the radius

• Arc length is independent of the radius