Trigonometry

4. Below are models for the number of hours of daylight in Seward, Alaska (60 degrees latitude) and New Orleans, Louisiana (30 degrees latitude). 

 

Seward  D=12.2 – 6.4cos[π(t + 0.2)/6] New Orleans D=12.2– 1.9cos[π(t + 0.2)/6] 

 

In these models, D represents the number of hours of daylight and t represents the month, with t=0 representing January 1.  

 

a. Graph both equations on the same xy plane. Be sure your graph is easy to read and labeled properly. Graphs can be created by hand or in excel but use a graphing calculator to aid. Be neat. 

 

 

  

 

 

 

 

 

 

 

 

 

 

 

b. Are there any critical values for either graph? Where are the intersections between the two? What do these intersections represent? 

 

 

 

c. Find the points where the hours of daylight are at a maximum/minimum. Around what time of the year are these points? Compare the information. 

 

 

 

d. What tools did you use to solve this problem? What other ways could you have come to find the same solution? 

 

 

 

e. How many hours of daylight are in each location at t=5? at t=8?