Arc Length and Angle Conversion

This video tutorial covers the topic of circles and small angles within trigonometry, focusing on calculating the length of an arc. The instructor explains the formula for arc length, emphasizing the importance of using radians for the angle. Several example problems are solved step-by-step, demonstrating how to apply the formula, convert angles from degrees to radians, and calculate exact or approximate values. The tutorial also covers finding the radius and angle of a sector, as well as calculating the perimeter of a sector.

What is the main focus of the lesson on circles and small angles?

• Determining the diameter of a circle

• Calculating the length of an arc

• Finding the area of a circle

• Measuring the circumference of a circle

In the equation for the length of an arc, what must the angle be measured in?

• Degrees

• Radians

• Gradians

• Revolutions

If the radius is 5 and the angle is 1.2 radians, what is the length of the arc?

• 8 cm

• 7 cm

• 6 cm

• 5.5 cm

When given an angle of pi/5 and a radius of 85 meters, what is the exact length of the arc?

• 17 pi meters

• 16 pi meters

• 18 pi meters

• 15 pi meters

How do you convert an angle from degrees to radians?

• Multiply by pi/180

• Subtract 180

• Add 180

• Multiply by 180/pi

What is the length of the arc when the radius is 9 and the angle is 40 degrees?

• 4 pi cm

• 2 pi cm

• 5 pi cm

• 3 pi cm

If the angle is 135 degrees, what is its equivalent in radians?

• 2 pi/3

• 3 pi/4

• 5 pi/6

• 4 pi/5

What is the length of the arc when the radius is 15 and the angle is 3 pi/4 radians, rounded to two decimal places?

• 36.55 meters

• 37.65 meters

• 35.45 meters

• 34.35 meters

Given an arc length of 12 pi and an angle of 0.8 pi radians, what is the radius?

• 12 meters

• 10 meters

• 15 meters

• 18 meters

If the angle is 30 degrees, what is its equivalent in radians?

• pi/6

• pi/5

• pi/4

• pi/7