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Lesson Example Discussion Quiz: Class Homework

Quiz In Class

Title: Angle measurement (degrees, radians)

Grade: 1300-a Lesson: S3-L6

Explanation: Hello Students, time to practice and review. Let us take next 10-15 minutes to solve the ten problems using the Quiz Sheet. Then submit the quiz to get the score. This is a good exercise to check your understanding of the concepts.

Quiz: in Class

Problem Id	Problem	Options
1	An electric motor spins at a rate of 1800 revolutions per hour. Through how many radians does it turn in 5 minutes?	A) 360π B) 300π C) 120π D) 60π
2	A wind farm operator needs to adjust the angles of the blades on a wind turbine for optimal performance based on wind direction. The blades initially face the wind at an angle of 135 degrees. Due to a shift in wind direction, the blades need to be adjusted to 315 degrees. The control software requires these angles to be input in radians.	A) \$(5pi)/4, (pi)/4\$ B) \$(3pi)/4, (7pi)/4\$ C) \$(3pi)/2, (7pi)/2\$ D) \$(3pi)/4, (7pi)/6\$
3	In a circle with center O, points A and B are two points on the circle. ∠AOB = 165°. Convert ∠AOB’s angle measure from degrees to radians.	A) \$( 13pi)/12\$ B) \$(7pi)/12\$ C) \$( 5pi)/12\$ D) \$( 11pi)/12\$
4	A Ferris wheel has a diameter of 50 meters. If a person sits in a carriage and moves around the circumference of the Ferris wheel by the \$120^∘\$, how far does the carriage travel in terms of radians?	A) \$ (2pi)/3\$ B) \$ (25pi)/3\$ C) \$ (5pi)/3\$ D) \$ (50pi)/3\$
5	Given three angles in degrees: 45°, 60°, and 75°, find the sum of these angles in radians.	A) \$ π/3\$ radians B) \$π/2\$ radians C) π radians D) 2π radians
6	Convert 2.5 radians to degrees, and then find the difference between this angle and 150 degrees.	A) 6.67° B) 7.6° C) 6.76° D) 7.66°
7	A pendulum swings through a maximum angle of 45 degrees on each side. If the length of the pendulum is 2 meters, what is the total distance traveled by the pendulum bob in one complete swing (from one extreme to the other and back)?	A) 3.14 m B) 4.13 m C) 3.41 m D) 4.31 m
8	Find the length of the arc intercepted by a central angle of 315 degrees in a circle of radius 36 cm.	A) 197.9 cm B) 179.7 cm C) 199.7 cm D) 177.9 cm
9	Given the angle 450°, convert it to radians. Then, find the sine and cosine of the resulting angle.	A) 1 and 3 B) 1 and 0 C) 0 and 2 D) 1 and 2
10	A regular hexagon is inscribed in a circle. What is the measure of the central angle subtended by one side of the hexagon, in degrees and radians?	A) \$pi/2\$ B) \$pi/3\$ C) \$pi/5\$ D) \$pi/5\$

Problem Id

Problem

Options

An electric motor spins at a rate of 1800 revolutions per hour. Through how many radians does it turn in 5 minutes?

A) 360π

B) 300π

C) 120π

D) 60π

A wind farm operator needs to adjust the angles of the blades on a wind turbine for optimal performance based on wind direction. The blades initially face the wind at an angle of 135 degrees. Due to a shift in wind direction, the blades need to be adjusted to 315 degrees. The control software requires these angles to be input in radians.

A) \$(5pi)/4, (pi)/4\$

B) \$(3pi)/4, (7pi)/4\$

C) \$(3pi)/2, (7pi)/2\$

D) \$(3pi)/4, (7pi)/6\$

In a circle with center O, points A and B are two points on the circle. ∠AOB = 165°. Convert ∠AOB’s angle measure from degrees to radians.

A) \$( 13pi)/12\$

B) \$(7pi)/12\$

C) \$( 5pi)/12\$

D) \$( 11pi)/12\$

A Ferris wheel has a diameter of 50 meters. If a person sits in a carriage and moves around the circumference of the Ferris wheel by the \$120^∘\$, how far does the carriage travel in terms of radians?

A) \$ (2pi)/3\$

B) \$ (25pi)/3\$

C) \$ (5pi)/3\$

D) \$ (50pi)/3\$

Given three angles in degrees: 45°, 60°, and 75°, find the sum of these angles in radians.

A) \$ π/3\$ radians

B) \$π/2\$ radians

C) π radians

D) 2π radians

Convert 2.5 radians to degrees, and then find the difference between this angle and 150 degrees.

A) 6.67°

B) 7.6°

C) 6.76°

D) 7.66°

A pendulum swings through a maximum angle of 45 degrees on each side. If the length of the pendulum is 2 meters, what is the total distance traveled by the pendulum bob in one complete swing (from one extreme to the other and back)?

A) 3.14 m

B) 4.13 m

C) 3.41 m

D) 4.31 m

Find the length of the arc intercepted by a central angle of 315 degrees in a circle of radius 36 cm.

A) 197.9 cm

B) 179.7 cm

C) 199.7 cm

D) 177.9 cm

Given the angle 450°, convert it to radians. Then, find the sine and cosine of the resulting angle.

A) 1 and 3

B) 1 and 0

C) 0 and 2

D) 1 and 2

A regular hexagon is inscribed in a circle. What is the measure of the central angle subtended by one side of the hexagon, in degrees and radians?

A) \$pi/2\$

B) \$pi/3\$

C) \$pi/5\$

D) \$pi/5\$