Approximating sin(0.5 degrees)

For small angles $\theta$ measured in radians, the approximation $\sin(\theta) \approx \theta$ holds true.

Angle Conversion

The given angle is $0.5^\circ$. We need to convert this angle from degrees to radians.

The formula for conversion is:

Radians = Degrees $\times \frac{\pi}{180}$

Therefore, $0.5^\circ$ in radians is:

$0.5 \times \frac{\pi}{180}$

Applying Approximation

Using the small angle approximation $\sin(\theta) \approx \theta$ with $\theta$ in radians:

$\sin(0.5^\circ) \approx 0.5 \times \frac{\pi}{180}$

Matching with Options

Comparing the result $0.5 \times \frac{\pi}{180}$ with the provided options:

• Option 1: $0.5$
• Option 2: $0.5 \times \frac{\pi}{90}$
• Option 3: $0.5 \times \frac{\pi}{180}$
• Option 4: $0.5 \times \frac{\pi}{360}$

The approximation $0.5 \times \frac{\pi}{180}$ matches Option 3.