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Put the steps for deriving the formula for the arc length of a circle in the correct order.

1. Write the formula for the circumference of a circle.
[tex]\[ C = 2 \pi r \][/tex]

2. Find the angle ratio that represents a percentage of the circle using the central angle, [tex]\(\theta\)[/tex].
[tex]\[ \frac{\theta}{360^{\circ}} \][/tex]

3. Multiply the angle ratio by the circumference to get the Arc Length Formula.
[tex]\[ \text{Arc Length} = \frac{\theta}{360^{\circ}} \cdot 2 \pi r \][/tex]



Answer :

GinnyAnswer
To derive the formula for the arc length of a circle, you should follow these steps in the correct order:

1. [tex]$\square$[/tex] Write the formula for the circumference of a circle.
2. [tex]$\square$[/tex] [tex]$C=2 \pi r$[/tex]
3. [tex]$\square$[/tex] Find the angle ratio that represents a percentage of the circle using the central angle, [tex]$\theta$[/tex]
4. [tex]$\square$[/tex] [tex]$\frac{\theta}{360^{\circ}}$[/tex]
5. [tex]$\square$[/tex] Multiply the angle ratio times the circumference to get the Arc Length Formula.
6. [tex]$\square$[/tex] Arc Length [tex]$=\frac{\theta}{360^{\circ}} \cdot 2 \pi r$[/tex]

By following these steps, you will derive the formula for calculating the arc length of a circle based on the central angle [tex]$\theta$[/tex] and the radius [tex]$r$[/tex] of the circle.

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