Arc Length and Central Angles

Walter Unob explains how to measure the arc or central angle of a circle. He introduces the concepts of arc and central angle, and describes their relationship. The video derives expressions for arc length in terms of radians and degrees, showing how to calculate one given the other. The tutorial concludes with a summary of the key points.

What is an arc in the context of a circle?

• A segment of the circle's circumference

• A line that divides the circle into two equal parts

• A point on the circle's edge

• A line segment from the center to the circumference

What is the central angle in a circle?

• The angle at the circumference

• The angle formed by two chords

• The angle formed by two radii

• The angle between a tangent and a radius

What is the formula for the circumference of a circle?

• C = 2πr

• C = πr²

• C = πd

• C = 2r

How many degrees are there in a full circle?

• 360°

• 90°

• 270°

• 180°

What is the total angle in radians for a full circle?

• π radians

• 2π radians

• 3π radians

• 4π radians

In the radians formula, what cancels out when relating arc length and central angle?

• The angle

• The arc length

• The radius

• The 2π

What is the relationship between arc length and central angle in radians?

• Arc length = radius / angle

• Arc length = angle × 2π

• Arc length = angle / radius

• Arc length = radius × angle

When using degrees, what is the divisor for the angle in the arc length formula?

• 270

• 90

• 360

• 180

What is the formula for arc length using degrees?

• Arc length = πrθ / 180

• Arc length = 2πrθ / 180

• Arc length = 2πrθ / 360

• Arc length = πrθ / 360

What is the equivalent expression for arc length in degrees?

• 2prθ / 360

• prθ / 180

• prθ / 360

• 2prθ / 180