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Lesson Example Discussion Quiz: Class Homework

Quiz At Home

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: at Home

Problem Id	Problem	Options
1	A car’s steering wheel turns at a rate of 3 revolutions per second. How many radians does it turn in 5 seconds?	A) \$(25\pi)\$ radians B) \$(30\pi)\$ radians C) \$(\pi)\$ radians D) \$(180\pi)\$ radians
2	A pendulum swings back and forth, completing 20 oscillations every 30 seconds. What is the total angular displacement of the pendulum in radians during this time?	A) \$(260\pi)\$ radians B) \$(40\pi)\$ radians C) \$(\pi/6)\$ radians D) \$(\pi/3)\$ radians
3	A spotlight on a theater stage moves at a rate of 180 degrees per minute. How many radians does it turn in 2 minutes and 30 seconds?	A) \$2.30/π\$ radians B) 2.30π radians C) 2π radians D) 2.5π radians
4	An airplane propeller spins at a rate of 2400 revolutions per minute. Through how many radians does it turn in 3 minutes?	A) 28450π radians B) 28686π radians C) 18110π radians D) 14400π radians
5	A point on the circumference of a circle with a radius of 5 meters subtends an angle of \$ (5π)/6 \$ radians at the center. What is the length of the corresponding arc?	A) \$ (21pi)/6 \$ B) \$ (29pi)/6 \$ C) \$ (25pi)/6 \$ D) \$ (23pi)/6 \$
6	In triangle ABC, angle A measures 60° and angle B measures 45°. Find the measure of angle C in both degrees and radians.	A) \$ 15°, (5pi)/12 \$ B) \$ 35°, (5pi)/12 \$ C) \$ 75°, (5pi)/12 \$ D) \$ 45°, (7pi)/12 \$
7	Convert the angle 315° to radians, then express the result as a fraction of \$ π \$.	A) \$ (7pi)/4 \$ B) \$ (5pi)/4 \$ C) \$ (7pi)/2 \$ D) \$ (5pi)/4 \$
8	A wheel makes 720 revolutions in one minute. Through how many radians does it turn in one second?	A) \$ 24pi \$ B) \$ 20pi \$ C) \$ 12pi \$ D) \$ 16pi \$
9	In a circle with center Q, points P and R lie on the circle. ∠PQR has a measure of \$ π/12 \$ rad. Convert ∠PQR’s angle measure from radians to degrees.	A) 45° B) 15° C) 75° D) 30°
10	A ladder is leaning against a wall. The angle formed between the ladder and the ground is \$ π/3 \$ radians, and the length of the ladder is 10 meters. What is the height at which the ladder touches the wall?	A) \$ 2sqrt3 \$ meters B) \$ 5sqrt3 \$ meters C) \$ 5sqrt5 \$ meters D) \$ 3sqrt3 \$ meters

Problem Id

Problem

Options

A car’s steering wheel turns at a rate of 3 revolutions per second. How many radians does it turn in 5 seconds?

A) \$(25\pi)\$ radians

B) \$(30\pi)\$ radians

C) \$(\pi)\$ radians

D) \$(180\pi)\$ radians

A pendulum swings back and forth, completing 20 oscillations every 30 seconds. What is the total angular displacement of the pendulum in radians during this time?

A) \$(260\pi)\$ radians

B) \$(40\pi)\$ radians

C) \$(\pi/6)\$ radians

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

A spotlight on a theater stage moves at a rate of 180 degrees per minute. How many radians does it turn in 2 minutes and 30 seconds?

A) \$2.30/π\$ radians

B) 2.30π radians

C) 2π radians

D) 2.5π radians

An airplane propeller spins at a rate of 2400 revolutions per minute. Through how many radians does it turn in 3 minutes?

A) 28450π radians

B) 28686π radians

C) 18110π radians

D) 14400π radians

A point on the circumference of a circle with a radius of 5 meters subtends an angle of \$ (5π)/6 \$ radians at the center. What is the length of the corresponding arc?

A) \$ (21pi)/6 \$

B) \$ (29pi)/6 \$

C) \$ (25pi)/6 \$

D) \$ (23pi)/6 \$

In triangle ABC, angle A measures 60° and angle B measures 45°. Find the measure of angle C in both degrees and radians.

A) \$ 15°, (5pi)/12 \$

B) \$ 35°, (5pi)/12 \$

C) \$ 75°, (5pi)/12 \$

D) \$ 45°, (7pi)/12 \$

Convert the angle 315° to radians, then express the result as a fraction of \$ π \$.

A) \$ (7pi)/4 \$

B) \$ (5pi)/4 \$

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

D) \$ (5pi)/4 \$

A wheel makes 720 revolutions in one minute. Through how many radians does it turn in one second?

A) \$ 24pi \$

B) \$ 20pi \$

C) \$ 12pi \$

D) \$ 16pi \$

In a circle with center Q, points P and R lie on the circle. ∠PQR has a measure of \$ π/12 \$ rad. Convert ∠PQR’s angle measure from radians to degrees.

A) 45°

B) 15°

C) 75°

D) 30°

A ladder is leaning against a wall. The angle formed between the ladder and the ground is \$ π/3 \$ radians, and the length of the ladder is 10 meters. What is the height at which the ladder touches the wall?

A) \$ 2sqrt3 \$ meters

B) \$ 5sqrt3 \$ meters

C) \$ 5sqrt5 \$ meters

D) \$ 3sqrt3 \$ meters