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?

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

Convert the angles from degrees to radians:

\$ "Radians" = "Degrees" times (pi)/180\$

Plug the starting angle in the formula

\$"Radians" = 30 times π/(180)\$

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

\$ "Radains" = pi/6\$

Plug the ending angle in the formula

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

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

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

Calculate the difference between the two angles:

Total angle swung through = Ending angle - Starting angle

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

\$= - (pi)/3\$

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 in total.

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

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

\$pi/2\$

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

\$pi/5\$

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

\$pi/6\$

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

\$pi/3\$

Option

D

Can you summarize what you’ve understood in the above steps?