The hours of daylight in LA oscillates from a low of 10 hours in Jan to 14 hours in July. How many months of the year are there more than 13 hours of daylight?
setting January is when t=0,
just solve
12 - 2cos(π/3 x) > 13
To determine how many months of the year in Los Angeles have more than 13 hours of daylight, we will need to analyze the range of daylight hours throughout the year.
The hours of daylight in LA range from a low of 10 hours in January to a high of 14 hours in July, as mentioned in the question. Since the hours of daylight gradually increase from January to July, we can assume that the months between January and July will have progressively more daylight hours.
Let's go through each month and compare the daylight hours:
January: 10 hours (less than 13 hours)
February: 11 hours (less than 13 hours)
March: 12 hours (less than 13 hours)
April: 13 hours (equal to 13 hours)
May: 14 hours (more than 13 hours)
June: 14 hours (more than 13 hours)
July: 14 hours (more than 13 hours)
From our analysis, we can see that starting from May until July (three months), Los Angeles has more than 13 hours of daylight. Therefore, there are three months in a year with more than 13 hours of daylight in LA.