How long is the arc subtended by an angle of 5pi/3 radians on a circle with a radius of 12 cm?
s = rθ = 12*5π/3 = 20π cm
To find the length of the arc subtended by an angle, you can use the formula:
Arc Length = Angle (in radians) * Radius
In this case, the angle is 5pi/3 radians and the radius is 12 cm.
Substituting these values into the formula, we get:
Arc Length = (5pi/3) * 12
Now, simplify the expression:
Arc Length = (5/3) * pi * 12
Arc Length = (5/3) * 12 * pi
Arc Length = 20 * pi
Therefore, the length of the arc subtended by an angle of 5pi/3 radians on a circle with a radius of 12 cm is 20pi cm.
To find the length of the arc subtended by an angle on a circle, you can use the formula:
Arc length = radius * angle
In this case, the given radius is 12 cm, and the given angle is 5π/3 radians.
First, let's calculate the length of the arc.
Arc length = 12 cm * (5π/3 radians)
To simplify the calculation, let's convert the angle from radians to degrees:
180 degrees = π radians
So, (5π/3) radians = (5π/3) * (180 degrees/π radians)
= 5 * 180 degrees / 3
= 900 degrees / 3
= 300 degrees
Now, let's substitute the values back into the formula:
Arc length = 12 cm * (300 degrees)
But we need to convert the degrees to radians to maintain consistency:
π radians = 180 degrees
So, (300 degrees) = (300 degrees) * (π radians / 180 degrees)
= 300 * π / 180 radians
= (5π/3) radians
Substituting this value back into the formula:
Arc length = 12 cm * (5π/3 radians)
Now we can calculate the arc length:
Arc length = 12 cm * (5π/3 radians)
≈ 20π cm
≈ 62.83 cm (rounded to two decimal places)
Therefore, the arc subtended by an angle of 5π/3 radians on a circle with a radius of 12 cm is approximately 62.83 cm.