# Activities

• • • ##### Subject Area

• Math: Precalculus: Trigonometry (Triangle and Circular Functions)

• ##### Author 9-12

60 Minutes

• ##### Software

TI InterActive!™

## The Light Side of Trigonometry

#### Activity Overview

In this activity, students use the TI InterActive!™ software to develop a model that determines the time of sunrise and sunset and the number of daylight hours in Melbourne on any day of the year. They also determine how the position on the Earth's surface affects the model equation.

#### Before the Activity

• Collect data for sunrise and sunset times in the city at regular intervals or on a specific day each month
• Install the TI InterActive!™ on the computer
• See the attached PDF file for detailed instructions for this activity
• Print pages 1 - 11 from the attached PDF file for the class
• #### During the Activity

Distribute the pages to the class.

• Open the Sun Cycle program and enter the latitude, longitude, and time zone for the city
• Record the data for sunrise and sunset
• Transfer the data into a TI InterActive!™ spreadsheet
• Enter appropriate formulas to calculate the total duration and the total number of daylight hours
• Prepare a statistical plot for the sunrise data
• Calculate a sinusoidal regression to determine a model for the total number of minutes between midnight and sunrise
• Graph the function along with the statistical plot
• Determine the amplitude, period, horizontal and vertical translations of the function
• Write an expression for the total number of minutes between midnight and sunrise
• Check the accuracy of the rule by determining the approximate sunrise time for today and verify with the actual value
• Repeat the procedure to obtain an expression for the city's sunset
• Calculate the number of daylight hours
• Graph sunrise, sunset, and daylight minutes on the same axes
• Determine the winter and summer solstice, and equinox dates from the model and check the accuracy
• Determine the average number of daylight hours per day for the whole year

• For a given longitude, latitude, and time zone, generate an equation to determine the number of daylight minutes
• Graph the daylight minutes for the Northern and Southern hemisphere
• Compare equations for the Northern and Southern hemisphere
• Compare table of values for different latitudes
• Observe that a different longitude does not affect the daylight time
• #### After the Activity

Students answer questions on the activity page.

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary