Radians and Arc Length Worksheet
Explore radians, arc length, and sector area with this Grade 12 trigonometry worksheet, featuring real-world problems and geometric diagrams.
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Radians and Arc Length
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the of the circle.
2. To convert degrees to radians, you multiply the degree measure by .
3. The formula for the arc length (s) of a circle is s = rθ, where r is the radius and θ is the angle in .
1. Convert 120° to radians.
π/3 radians
2π/3 radians
π/2 radians
3π/2 radians
2. What is the arc length of a circle with a radius of 5 cm and a central angle of 3 radians?
5 cm
8 cm
15 cm
1.67 cm
1. A pizza has a radius of 20 cm. A slice of pizza has a central angle of 45°. What is the length of the crust (arc length) for this slice? (Round to two decimal places)
2. An industrial fan has blades that are 1.5 meters long. If the fan rotates at 100 revolutions per minute, what is the angular speed of the blade tips in radians per second?
1. A central angle of 2π radians is equivalent to 360 degrees.
True
False
2. The area of a sector of a circle with radius 'r' and central angle 'θ' (in radians) is given by the formula A = rθ.
True
False
1. A car tire has a diameter of 60 cm. If the car travels 100 meters, how many revolutions does the tire make? (Round to the nearest whole number)
2. A pendulum of length 50 cm swings through an angle of 30° on each side of the vertical. What is the total length of the arc traced by the pendulum bob in one full swing (from one extreme to the other and back)?
