Trigonometry -Lab Hours of Daylight

Therefore , the amplitude of the cosine function (model ) will be

Hours

The vertical shift will be

Hours Figure 3 : Scatterplot of the number of daylight hours for Fairbanks Alaska

Figure 3 shows the scatterplot for Fairbanks , Alaska with day of year t as the independent variable and number of hours of daylight , H as the dependent variable

From figure 3 , for day 0 , the value of daylight hours is 3 .7 hours therefore , the phase shift of the cosine function will be equal to 180o or ? radians . In

addition , since , number of hours of daylight at the end of the year and at start of the year is same therefore , the period of the cosine function will be 2 ? or 360o Therefore , the cosine function for the number of daylight hours for Boston will be given byFigure 4 : Cosine function model of the number of daylight hours for Fairbanks , Alaska

for Fairbanks with day of year t , as the independent variable and number of hours of daylight , H as the dependent variable . From figure 4 it can be seen that both scatterplot and graph of the cosine function shows approximately same cycle for the number of hours of daylight Therefore , modeled function can be used for calculating number of hours of daylight for any given day for Fairbanks , Alaska (64N

Difference in Equation of Boston and Fairbanks and Other Cities

The equation of the Boston and Fairbanks areThe only difference in above equation for Boston and Fairbanks is in amplitude of the cosine function . For Boston , the amplitude is 3 .1 hours and for Fairbanks , the amplitude is 8 .5 hours . Therefore , the amplitude of daylight hours increases as the latitude of the place increases

The only parameter that will change if the data is given for Tromso Norway , which...