Question

Cheyenne, Wyoming, has a latitude of 41° N. At this latitude, the number of hours of daylight D can be modeled by

D = 2.914 sin(0.017t − 1.321) + 12.134
where t represents the day, with
t = 1
corresponding to January 1. Use a graphing utility to determine the days on which there are more than 10 hours of daylight.(Round your answers to the nearest integer.)

Answer 1

To determine the days with more than 10 hours of daylight in Cheyenne, Wyoming, we can use the given equation and solve for t. Using a graphing utility or calculator, we can find the approximate days.

Step-by-step explanation:

To determine the days on which there are more than 10 hours of daylight at latitude 41° N in Cheyenne, Wyoming, we can use the given equation D = 2.914 sin(0.017t − 1.321) + 12.134, where D represents the number of hours of daylight and t represents the day, with t = 1 corresponding to January 1.

To find the days with more than 10 hours of daylight, we need to solve the equation D > 10.

1. Substitute 10 for D in the equation: 10 = 2.914 sin(0.017t − 1.321) + 12.134
2. Subtract 12.134 from both sides: -2.134 = 2.914 sin(0.017t − 1.321)
3. Divide both sides by 2.914: -0.733 = sin(0.017t − 1.321)
4. Take the arcsin of both sides to solve for t: 0.017t − 1.321 = arcsin(-0.733)
5. Add 1.321 to both sides: 0.017t = arcsin(-0.733) + 1.321
6. Divide both sides by 0.017: t = (arcsin(-0.733) + 1.321) / 0.017

Using a graphing utility or a scientific calculator, we can plug in the value for t to find the approximate day when there are more than 10 hours of daylight. The result will be rounded to the nearest integer.