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Lesson Example Discussion Quiz: Class Homework

Quiz In Class

Title: Angle measurement (degrees, radians)

Grade: 1400-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	A carousel rotates at a speed of 45 revolutions per minute. How many radians does it turn in 1 minute and 20 seconds?	A) 240π B) 120π C) 75π D) 25°
2	A satellite communication company is calibrating a new dish to improve signal reception. The dish needs to be precisely aimed. First, it must be pointed at an angle of 45 degrees to lock onto a satellite in the eastern sky. Later, for a satellite in the western sky, the dish needs to be adjusted to 270 degrees. The angles must be converted to radians for the dish’s motor control system.	A) \$ pi/4, (2pi)/3\$ B) \$ pi/4, (3pi)/2\$ C) \$ pi/2, (3pi)/2\$ D) \$ (3pi)/4, (5pi)/4\$
3	In a right triangle, one of the angles is given as 0.4 radians. Find the other non-right angle in both degrees and radians.	A) 57.08 degrees or \$π/4 − 0.4\$ radians B) 71.08 degrees or \$π/2 + 0.4\$ radians C) 51.08 degrees or \$π/3 − 1.4\$ radians D) 67.08 degrees or \$π/2 − 0.4\$ radians
4	Given \$ θ = (7pi)/6\$, convert this to degrees and then determine the exact values of \$ "sin"^(-1) ("sin"(θ)) \$ and \$"cos"^(-1)("cos"(θ))\$.	A) \$ - pi/3, (3pi)/4\$ B) \$ pi/3, (2pi)/3\$ C) \$ pi/4, - (7pi)/6\$ D) \$ - pi/6, (5pi)/6\$
5	An architect is designing a circular building with a radius of 50 meters. They need to determine the angle subtended by an arc of 20 meters on the circumference of the building. To ensure precision in the design, they want this angle both in degrees and radians.	A) \$31.92^∘\$ and 1.4 radians B) \$25.92^∘\$ and 0.2 radians C) \$22.92^∘\$ and 0.4 radians D) \$21.29^∘\$ and 2.1 radians
6	A circle with a radius of 10 meters has a chord that is 12 meters long. Calculate the length of the arc between the ends of the chord and the angle subtended by this arc in both degrees and radians.	A) 1.268 radians, 73.47° and 12.87 m B) 1.628 radians, 73.74° and 12.78 m C) 1.286 radians, 73.74° and 12.87 m D) 1.628 radians, 74.74° and 12.78 m
7	In triangle ABC, angle A is twice angle B, and angle C is 40 degrees less than angle A. Find the measures of angles A, B, and C in degrees and radians.	A) \$(22pi)/45 ,(11pi)/45, (4pi)/15\$ B) \$(22pi)/54 ,(11pi)/45, (4pi)/15\$ C) \$(22pi)/45 ,(11pi)/54, (4pi)/15\$ D) \$(22pi)/45 ,(11pi)/45, (4pi)/45\$
8	Find the sum of the angles \$(2pi)/90\$ radians and \$3((5pi)/30)\$ radians, and express the result in degrees.	A) 94° B) 40° C) 49° D) 90°
9	In a right triangle, the lengths of the sides are 3, 4, and 5. Find the angles in radians.	A) 0.463 , 0.927 B) 0.643 , 0.927 C) 0.463 , 0.729 D) 0.634 , 0.972
10	Find the degree measure of the angle subtended at the center of a circle of radius 100 cm by an arc of length 22 cm.	A) 21°36' B) 12°36' C) 21°63' D) 12°63'

Problem Id

Problem

Options

A carousel rotates at a speed of 45 revolutions per minute. How many radians does it turn in 1 minute and 20 seconds?

A) 240π

B) 120π

C) 75π

D) 25°

A satellite communication company is calibrating a new dish to improve signal reception. The dish needs to be precisely aimed. First, it must be pointed at an angle of 45 degrees to lock onto a satellite in the eastern sky. Later, for a satellite in the western sky, the dish needs to be adjusted to 270 degrees. The angles must be converted to radians for the dish’s motor control system.

A) \$ pi/4, (2pi)/3\$

B) \$ pi/4, (3pi)/2\$

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

D) \$ (3pi)/4, (5pi)/4\$

In a right triangle, one of the angles is given as 0.4 radians. Find the other non-right angle in both degrees and radians.

A) 57.08 degrees or \$π/4 − 0.4\$ radians

B) 71.08 degrees or \$π/2 + 0.4\$ radians

C) 51.08 degrees or \$π/3 − 1.4\$ radians

D) 67.08 degrees or \$π/2 − 0.4\$ radians

Given \$ θ = (7pi)/6\$, convert this to degrees and then determine the exact values of \$ "sin"^(-1) ("sin"(θ)) \$ and \$"cos"^(-1)("cos"(θ))\$.

A) \$ - pi/3, (3pi)/4\$

B) \$ pi/3, (2pi)/3\$

C) \$ pi/4, - (7pi)/6\$

D) \$ - pi/6, (5pi)/6\$

An architect is designing a circular building with a radius of 50 meters. They need to determine the angle subtended by an arc of 20 meters on the circumference of the building. To ensure precision in the design, they want this angle both in degrees and radians.

A) \$31.92^∘\$ and 1.4 radians

B) \$25.92^∘\$ and 0.2 radians

C) \$22.92^∘\$ and 0.4 radians

D) \$21.29^∘\$ and 2.1 radians

A circle with a radius of 10 meters has a chord that is 12 meters long. Calculate the length of the arc between the ends of the chord and the angle subtended by this arc in both degrees and radians.

A) 1.268 radians, 73.47° and 12.87 m

B) 1.628 radians, 73.74° and 12.78 m

C) 1.286 radians, 73.74° and 12.87 m

D) 1.628 radians, 74.74° and 12.78 m

In triangle ABC, angle A is twice angle B, and angle C is 40 degrees less than angle A. Find the measures of angles A, B, and C in degrees and radians.

A) \$(22pi)/45 ,(11pi)/45, (4pi)/15\$

B) \$(22pi)/54 ,(11pi)/45, (4pi)/15\$

C) \$(22pi)/45 ,(11pi)/54, (4pi)/15\$

D) \$(22pi)/45 ,(11pi)/45, (4pi)/45\$

Find the sum of the angles \$(2pi)/90\$ radians and \$3((5pi)/30)\$ radians, and express the result in degrees.

A) 94°

B) 40°

C) 49°

D) 90°

In a right triangle, the lengths of the sides are 3, 4, and 5. Find the angles in radians.

A) 0.463 , 0.927

B) 0.643 , 0.927

C) 0.463 , 0.729

D) 0.634 , 0.972

Find the degree measure of the angle subtended at the center of a circle of radius 100 cm by an arc of length 22 cm.

A) 21°36'

B) 12°36'

C) 21°63'

D) 12°63'