Central Angles, Arcs, Arc Length, Area of Sectors 2024

Front

What is a central angle?

Back

A central angle is an angle whose vertex is at the center of a circle and whose sides (rays) intersect the circle at two points.

Front

Define an arc in a circle.

Back

An arc is a portion of the circumference of a circle, defined by two endpoints on the circle.

Front

What is the formula for arc length?

Back

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

Front

How do you calculate the area of a sector?

Back

The area (A) of a sector can be calculated using the formula: A = (θ/2π) * πr² = (θ/2) * r², where θ is in radians.

Front

What is the relationship between the measure of an arc and its central angle?

Back

The measure of an arc in degrees is equal to the measure of its central angle.

Front

If the central angle is 90 degrees, what is the length of the arc in a circle with a radius of 10 units?

Back

Using the formula L = r * θ, convert 90 degrees to radians (θ = π/2). Thus, L = 10 * (π/2) = 5π units.

Front

What is the measure of a semicircle?

Back

The measure of a semicircle is 180 degrees.

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 area of a sector with a central angle of 60 degrees and a radius of 5 units?

Back

Convert 60 degrees to radians: θ = π/3. Then, A = (θ/2) * r² = (π/3)/2 * 5² = (5π/3) * 25/2 = (25π/6) square units.

Front

What is the formula for the circumference of a circle?

Back

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