Question

what is the angle swept out by the second hand of a clock in a 30 - second interval? express your answer in both degrees and radians.
degrees:
radians:

Explanation:

Step1: Calculate the angle in degrees

The second - hand of a clock makes a full rotation (\(360^{\circ}\)) in \(60\) seconds.
Let \(\theta_d\) be the angle in degrees. Using the proportion \(\frac{\theta_d}{30}=\frac{360^{\circ}}{60}\)

$$ \theta_d=\frac{360^{\circ}\times30}{60}= 180^{\circ} $$

Step2: Convert degrees to radians

Use the conversion formula \(\theta_r=\frac{\pi}{180}\times\theta_d\), where \(\theta_r\) is the angle in radians and \(\theta_d = 180^{\circ}\)

$$ \theta_r=\frac{\pi}{180}\times180=\pi $$

Answer:

Degrees: \(180\)
Radians: \(\pi\)