Download Trig Function Application Question

Math 30-1
Trigonometric Functions
Name: ___________________
Applying Trigonometric Functions: Hours of Daylight
Specific Outcome
T 4: Graph and analyze the trigonometric functions
sine, cosine, and tangent to solve problems.
Questions
all
Mark
20

An application of sinusoidal functions is the number of hours of daylight over a full year. The
table below shows the number of hours of daylight on the 21st day of each month for Edmonton,
AB. June 21 is the longest day of the year and December 21 is the shortest day of the year.
Hours of Daylight for Edmonton, AB
Jan 21
day 21
Feb 21
day 52
Mar 21
day 80
Apr 21
day
111
May 21
day
141
Jun 21
day
172
Jul 21
day
202
Aug 21
day
233
Sep 21
day
264
Oct 21
day
294
Nov 21
day
325
Dec 21
day
355
8.33
10.27
12.32
14.50
16.27
17.03
16.23
14.37
12.22
10.13
8.25
7.45

Draw a scatterplot for the number of hours of daylight, y, in Edmonton on the day of the
year, x. Make sure to label and scale the axes. (4 marks)

Determine the amplitude and median of this data. (2 marks)
Math 30-1
Trigonometric Functions

Determine the period and b value of this data. (2 marks)

Use the information above to write a sinusoidal function that models the number of hours of
daylight. Don’t forget about the phase shift! You will have to choose whether a sine or cosine
model is better – try to choose the one with the minimum phase shift. (4 marks)

Draw a graph of the function that models the number of daylight hours in Edmonton on your
calculator and on the grid on the first page. Use your calculator to make sure the maximum,
minimum, and median points are accurate. (You will know if you have a correct equation if
it follows the points on the scatterplot well.) (4 marks)

Use the equation of the function to estimate the amount of daylight on your birthday. Give
the answer in hours and minutes to the nearest minute. (2 marks)
My birthday is _________________.

Use your calculator to determine how many days of the year Edmonton has over 16 hours of
daylight. (2 marks)