Exploring Arc Length and Sector Area

The video tutorial covers finding arc length and sector area using radians. It begins with an introduction to the concepts and proceeds with examples of calculating arc length and determining radius from given arc lengths. The tutorial also addresses handling complex angles and converting them into radians. Finally, it demonstrates calculating sector area using different angles, emphasizing the use of radians throughout.

How do you convert 120 degrees to radians?

• 2π/3

• π/2

• π/6

• π/3

What is the arc length when the radius is 12 and the angle is 60 degrees?

• 8π

• 4π

• 2π

• 6π

If the diameter of a circle is 24, what is the radius?

• 14

• 12

• 10

• 8

Given an arc length of 5π and an angle of 30 degrees, what is the radius?

• 15

• 20

• 25

• 30

For an angle of 70 degrees, what is the radian measure?

• 7π/18

• π/4

• π/6

• 2π/3

Given an arc length of 5π and an angle of 30 degrees, how do you set up the equation to find the radius?

• π/2 * r = 5π

• 2π/3 * r = 5π

• π/3 * r = 5π

• π/6 * r = 5π

What is the sector area when the radius is 16 and the angle is 90 degrees?

• 48π

• 128π

• 32π

• 64π

How do you calculate the sector area for a radius of 8 and an angle of 135 degrees?

• 48π

• 36π

• 24π

• 12π

What is the formula for finding the sector area in radians?

• 1/2 r^2θ

• 2πrθ

• r^2/θ

• πr^2θ

What is the sector area for a radius of 18 and an angle of 40 degrees?

• 18π

• 36π

• 54π

• 72π