Arc Length

Front

What is the formula for arc length?

Back

Arc Length = r * θ, where r is the radius and θ is the angle in radians.

Tags

CCSS.HSG.C.B.5

Front

How do you convert degrees to radians?

Back

To convert degrees to radians, multiply by π/180.

Tags

CCSS.HSF.TF.A.1

Front

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

Back

The arc length is directly proportional to the radius; as the radius increases, the arc length increases.

Tags

CCSS.HSG.C.B.5

Front

If the central angle is 0 radians, what is the arc length?

Back

The arc length is 0, as there is no distance covered.

Tags

CCSS.HSG.C.B.5

Front

What is the arc length of a circle with a radius of 5 cm and a central angle of π/2 radians?

Back

Arc Length = 5 * (π/2) = 2.5π cm.

Tags

CCSS.HSG.C.B.5

Front

How do you find the arc length when given the angle in degrees?

Back

Convert the angle to radians first, then use the formula Arc Length = r * θ.

Tags

CCSS.HSG.C.B.5

Front

What is the arc length of a circle with a radius of 10 cm and a central angle of 3 radians?

Back

Arc Length = 10 * 3 = 30 cm.

Tags

CCSS.HSG.C.B.5

Front

What is the significance of the unit circle in understanding arc length?

Back

The unit circle helps visualize the relationship between angles and arc lengths, as the radius is 1.

Front

How do you find the arc length of a sector of a circle?

Back

Arc Length = (θ/2π) * Circumference of the circle.

Tags

CCSS.HSG.C.B.5

Front

What is the circumference of a circle with a radius of 4 cm?

Back

Circumference = 2π * 4 = 8π cm.

Tags

CCSS.7.G.B.4