Teacher notes
The focus of this PullOut is using
sinusoidal models to estimate the
length of daylight and the sun’s declination
and altitude over time in
various locations in the Northern
Hemisphere. In Activity 1, students
work with a data set that consists of
day number and length of daylight
for Boston, Massachusetts. Based on
these data, they determine a sinusoidal
model of the form
f (x)=Asin(B(x–C))+D
for estimating length of daylight
given day number, x. They compare
their model to one determined using
a graphing calculator’s regression
capabilities and must grapple with
an output from regression that specifies
models in an alternate form,
asin(bx + c) + d. In Activity 2, students
determine models for estimating
length of daylight at various locations
using sunrise/sunset data from only two days, the winter and summer
solstices. In an effort to understand
Seasonal Affective Disorder (SAD), students
use their models to estimate the
length of daylight and instantaneous
rate of change in daylight for specific
dates. When graphing models in
Activities 1 and 2, calculators must be in
radian mode. In Activity 3, attention
shifts to models that estimate solar declination
(in degrees) as seen from Earth
and the elevation (in degrees) of the sun
above the horizon. These models
involve both sine and cosine functions.
