83 has an apparent diameter of angular size of 0.22°.(i) What is its angular size in radians?

1. Break Down the Problem

To convert the angular size from degrees to radians, we need to use the relationship between degrees and radians. The formula to convert degrees to radians is: $\text{radians} = \text{degrees} \times \frac{\pi}{180}$

2. Relevant Concepts

• Angular Size in Degrees: Given as $0.22^\circ$.
• Conversion Factor: $\frac{\pi}{180}$ is the conversion factor from degrees to radians.

3. Analysis and Detail

Now, we apply the conversion formula using the given angular size:

1. Multiply the angular size in degrees by the conversion factor: $\text{radians} = 0.22 \times \frac{\pi}{180}$

4. Verify and Summarize

Calculating this step: $\text{radians} = 0.22 \times \frac{\pi}{180} \approx 0.22 \times 0.0174533 \approx 0.0038397 \text{ radians}$

Final Answer

The angular size of 83 in radians is approximately $0.00384 \text{ radians}$.