1

Problem

A pendulum swings from a 30-degree angle on one side to a 30-degree angle on the other side, covering a total arc of 60 degrees. How many radians does the pendulum swing through in total?

2

Step

The given angles are

Starting angle = 30 , Ending angle = - 30 (since the pendulum swings to the other side, it’s equivalent to -30 degrees) and total arc = 60 degrees

3

Formula

Convert the angles from degrees to radians: \$ "Radians" = "Degrees" \times (pi)/(180)\$

4

Step

Plug the starting angle in the formula:

\$"Radians" = 30 \times π/(180)\$​

\$"Radius" = \cancel(30) \times (pi) / \cancel(180)^6\$

\$"Radains" = (pi)/6\$

5

Step

Plug the ending angle in the formula:

\$"Radians" = - 30 \times (pi)/(180)\$

\$"Radians" = \cancel( -30) \times (pi)/ \cancel(180)^6\$

\$"Radians" = - (pi)/6\$

6

Step

Calculate the difference between the two angles:

Total angle swing through = Ending angle - Starting angle

\$= - (pi)/6 - (pi)/6\$

\$ - (pi)/3\$ radians

7

Hint

So, the pendulum swings through \$- π/3\$​ radians in total. Since the direction doesn’t matter for the total angle covered, we don’t consider the negative sign when talking about the total magnitude of the angle. Therefore, the pendulum swings through the \$π/3\$ radians.

8

Solution

Therefore, the pendulum swings through the \$π/3\$ radians in total.

9

Sumup

Please summarize Problem, Clue, Hint, Formula, Steps and Solution

Choices

10

Choice-A

\$π/2\$​ is incorrect because \$π/2\$​ radians would correspond to a 90-degree arc, which is greater than the given 60-degree arc

Wrong \$pi/2\$ radians

11

Choice-B

Incorrect: Because \$π/5\$​ would be the equivalent of approximately 36 degrees, which exceeds the total arc covered by the pendulum

Wrong \$pi/5\$ radians

12

Choice-C

\$π/6\$ is incorrect because it corresponds to half of the total arc covered by the pendulum, not the total radians swing through

Wrong \$pi/6\$ radians

13

Choice-D

The calculation using the formula confirms that \$pi/3\$ is the correct value

Correct \$pi/3\$ radians

14

Answer

Option

D

15

Sumup

Please summarize choices