To change the formula for the area of a sector of a circle from degrees to radians, we need to follow these steps in order:
1. Write the formula for a sector area of a circle with central angle, [tex]\(\theta\)[/tex], in degrees.
2. Area of a Sector [tex]\(=\frac{\theta}{360^{\circ}} \cdot \pi r^2\)[/tex]
3. Replace [tex]\(360^{\circ}\)[/tex] with [tex]\(2 \pi\)[/tex] radians.
4. Area of a Sector [tex]\(=\frac{\theta}{2 \pi} \cdot \pi r^2\)[/tex]
5. Replace the angle ratio in degrees with the angle ratio in radians in the formula.
6. [tex]\(\frac{\theta}{360^{\circ}}=\frac{\theta}{2 \pi}\)[/tex]
7. Simplify by canceling.
8. Area of a Sector [tex]\(=\frac{1}{2} \theta r^2\)[/tex]
So, the correct order of the steps is:
[tex]\[
\begin{array}{c}
\text{1. Write the formula for a sector area of a circle with central angle, } \theta \text{, in degrees.} \\
\text{2. Area of a Sector } = \frac{\theta}{360^{\circ}} \cdot \pi r^2 \\
\text{3. Replace } 360^{\circ} \text{ with } 2 \pi \text{ radians.} \\
\text{4. Area of a Sector } = \frac{\theta}{2 \pi} \cdot \pi r^2 \\
\text{5. Replace the angle ratio in degrees with the angle ratio in radians in the formula.} \\
\text{6. } \frac{\theta}{360^{\circ}} = \frac{\theta}{2 \pi} \\
\text{7. Simplify by canceling.} \\
\text{8. Area of a Sector } = \frac{1}{2} \theta r^2 \\
\end{array}
\][/tex]
