findAngleBetweenClockHands()

Step 1: Understand the nature of the problem

The first step in solving this problem is understanding the nature of the problem itself. We need to calculate the angle between the hour and minute hands on a clock. We know the clock hands revolve 360 degrees and there are 12 hours or 60 minutes. These facts will help us in our calculations.

Step 2: Calculation logic

We first need to find the positions of the hour and minute hands. The minute hand moves 360 degrees in 60 minutes, therefore, for each minute, it moves 6 degrees (360 / 60). We need to do the same for hour hand. For the hour hand, we know that it moves 360 degrees in 12 hours. Therefore, for each minute it moves 0.5 degree (360 / (12 * 60)).

let minuteHandAngle = Double(minutes) * 6
let hourHandAngle = Double((hours % 12) * 60 + minutes) * 0.5

Step 3: Calculate the angle

Next, we subtract the smaller angle from the larger one to get the degree difference between the two hands. This will give us the smaller angle between the two hands. If we want to find the larger angle, we can subtract our result from 360.

let angle = max(hourHandAngle, minuteHandAngle) - min(hourHandAngle, minuteHandAngle)

Step 4: Write the final function

Once we have completed our calculations, we can write our final function. We need to make sure our hour and minute inputs are valid.

func findAngle(hours: Int, minutes: Int) -> Double {
    if hours < 0 || minutes < 0 || hours > 12 || minutes > 60 { return -1 }
    let minuteHandAngle = Double(minutes) * 6
    let hourHandAngle = Double((hours % 12) * 60 + minutes) * 0.5
    let angle = max(hourHandAngle, minuteHandAngle) - min(hourHandAngle, minuteHandAngle)
    return min(360 - angle, angle)
}

Conclusion

This function will now correctly calculate the smaller angle between the hour and minute hands of a clock. Given the time (in hours and minutes), this function will return the smaller angle in degrees. Keep in mind that it will return -1 for invalid input hours or minutes.