Write a formula for converting hours, starting with midnight as zero, to a decimal number of degrees. Assume that a full day equals 360º, 60 minutes equals one hour, and 60 seconds equals one minute. Use x, y, and z to represent hours, minutes, and seconds respectively. Use T for the decimal number of degrees.
T = 360(x + y + z)
T = 60(x + y + z)
T = 15(x + y/60 + z/3600)
That is fine assuming a 24 hour clock (military time) of course.
Damon, yes. Military time.
To convert hours to a decimal number of degrees, you need to consider the relationship between time and a full circle, which is 360 degrees.
First, let's start by converting hours, minutes, and seconds into a common unit, which is seconds.
To convert hours, we know that 1 hour is equal to 60 minutes and 1 minute is equal to 60 seconds. So, the total number of seconds can be calculated as:
Total Seconds = (hours * 60 * 60) + (minutes * 60) + seconds
Next, we need to determine the proportion of a full circle that corresponds to the total seconds. Since there are 24 hours in a day, and we want to consider starting from midnight as zero, we divide the total seconds by the total seconds in a day:
Proportion of Full Circle = Total Seconds / (24 * 60 * 60)
Finally, we can multiply the proportion of a full circle by 360 degrees to get the decimal degree value:
Decimal Degrees = Proportion of Full Circle * 360 degrees
Combining these steps, the formula for converting hours to a decimal number of degrees is:
T = (Total Seconds / (24 * 60 * 60)) * 360
Simplifying this formula, we can get:
T = (Total Seconds / 86400) * 360
In this formula, T represents the decimal number of degrees. Replace "Total Seconds" with the appropriate value according to the time you want to convert, and you'll get the desired result.