Arc Length

Front

What is the formula for arc length?

Back

The arc length (L) of a circle can be calculated using the formula: L = rθ, where r is the radius and θ is the angle in radians.

Front

How do you convert degrees to radians?

Back

To convert degrees to radians, use the formula: radians = degrees × (π/180).

Front

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

Back

The arc length is directly proportional to the radius of the circle. As the radius increases, the arc length increases.

Front

What is a minor arc?

Back

A minor arc is an arc that is smaller than a semicircle, measuring less than 180 degrees.

Front

What is a major arc?

Back

A major arc is an arc that is larger than a semicircle, measuring more than 180 degrees.

Front

If the radius of a circle is 10 ft and the angle is 30 degrees, what is the arc length?

Back

First, convert 30 degrees to radians: 30 × (π/180) = π/6. Then, use the formula: L = rθ = 10 × (π/6) = (10π/6) ft = (5π/3) ft.

Front

What is the circumference of a circle?

Back

The circumference (C) of a circle is given by the formula: C = 2πr, where r is the radius.

Front

How do you find the angle in radians if you know the arc length and radius?

Back

Use the formula: θ = L/r, where L is the arc length and r is the radius.

Front

What is the measure of a full circle in radians?

Back

A full circle measures 2π radians.

Front

If an arc length is 15.8π ft and the radius is 10 ft, what is the angle in radians?

Back

Using the formula θ = L/r, we have θ = (15.8π)/(10) = 1.58π radians.