If A = $\frac{\theta}{360}$$\pi r^2$, make $\theta$ the subject of the formula

To make $\theta$ the subject of the formula, we need to isolate it on one side of the equation. Here is the step-by-step breakdown:

1. Analyze the equation

The given equation is:

Our goal is to get $\theta$ by itself. Currently, $\theta$ is being multiplied by $\pi r^2$ and divided by $360$.

2. Explain the concept

To isolate a variable, we perform inverse operations. If a term is dividing, we multiply it to the other side. If a term is multiplying, we divide it to the other side.

3. Show the solution

Step 1: Multiply both sides by 360 to remove the fraction.

Step 2: Divide both sides by $(\pi r^2)$ to isolate $\theta$.

Rearranging this to put $\theta$ on the left side:

4. Identify the answer

Comparing our result to the given options: A. $\theta = \frac{360}{\pi A}$ B. $\theta = \frac{360A}{\pi \theta}$ C. $\theta = \frac{360A}{\pi r^2}$ D. $\theta = \frac{360 r^2}{\pi A}$

The correct option is C.

5. Exam Tip

When asked to "make a variable the subject," treat the equation like a balance scale. Whatever operation you perform to move terms away from your target variable, you must apply it to the entire opposite side. Also, always check your final expression to ensure the target variable ($\theta$) does not appear on the right-hand side of the final answer!