A 1.25 m long pendulum swings 5.75 degrees on each side of the vertical. Find the length of arc traveled by the end of the pendulum.

So your pendulum swings through 11.5°

use ratios
whole circumference/360 = arc/11.5
arc = (11.5/360)(circumference of whole circle)

To find the length of the arc traveled by the end of the pendulum, we need to use the formula for arc length.

The formula for arc length is:

Arc length = (θ/360) * (2π * r)

where θ is the angle in degrees, r is the radius of the circle, and π is approximately 3.14159.

In this case, the angle is given as 5.75 degrees, and the length of the pendulum is given as 1.25 meters.

First, let's convert the angle from degrees to radians. We know that 180 degrees is equivalent to π radians, so to convert from degrees to radians, we divide the angle by 180 and multiply by π.

θ in radians = (5.75/180) * π

θ in radians = 0.031818 * π

Now we can substitute the values into the formula:

Arc length = (0.031818 * π/360) * (2π * 1.25)

Arc length = (0.031818/360) * (2 * 3.14159 * 1.25)

Arc length = (0.088383) * (7.853975)

Arc length = 0.693989

Therefore, the length of the arc traveled by the end of the pendulum is approximately 0.693989 meters.

To find the length of the arc traveled by the end of the pendulum, we can use trigonometry.

The arc length formula for a circular sector is given by:

Arc Length = r * θ

where r is the radius of the circle (in this case, the length of the pendulum) and θ is the angle (in radians) subtended by the arc.

First, let's convert the given angle from degrees to radians. Since there are 180 degrees in π radians, we can calculate:

θ (in radians) = θ (in degrees) * (π / 180)

In this case, θ = 5.75 degrees, so:

θ (in radians) = 5.75 * (π / 180)

Next, we substitute the values into the formula:

Arc Length = r * θ

In this case, r = 1.25 m (given)

Arc Length = 1.25 * (5.75 * (π / 180))

Now, we can calculate the arc length:

Arc Length ≈ 0.04415 m

Therefore, the length of the arc traveled by the end of the pendulum is approximately 0.04415 meters.