Exploring the Sine and Cosine Curve
Main Image
Main Image
Created by
University of British Columbia - Vancouver
Activity Language
Grade
Time Needed for Activity
Subjects
To pictorially demonstrate the relationship between the sine and cosine graphs and the unit circle. This will give the students a better idea of what the graphs should look like rather than having them memorize it.
What You Need
- Dry spaghetti (dime-sized bundle)
- String or yarn cut out - 30 cm long piece per student
- Legal size paper - one per student
- Copies of the unit circle template - one per pair of students (see attachment "Trig Circle Template")
- Tape
- Sharpies, or other dark markers - one per pair of students
- Protractors - one per pair of students
Guide:
Safety Notes
Ensure you are familiar with Let's Talk Science's precautions with respect to safe outreach to youth.
What To Do
Activity - Sine and Cosine Spaghetti
- Have the students form groups of 2. Give each group 1 circle template, a couple pieces of dry spaghetti, 2 already cut out piece of string, and 2 pieces of legal sized paper.
- Have the students wrap the string around the circle, with the string starting from the positive x-axis, then taping it in place
- Using a protractor, label some of the most used angles: ie: the angles with 0, π/6, π/4, π/3 and π/2 as the reference angle (in degrees, angles with 0°, 30°, 45°, 60° and 90° as the reference angle). These labels should be drawn both on the page AND the string
- Have the students lay out the string straight across their piece of legal sized paper. They will have marks along the string indicating 0, π/6, π/4, π/3, π/2, etc. Now have the students locate these marks on the unit circle, and measure the distance from the x-axis, and the marker they drew for each angle. Make them break off the spaghetti at that distance, and place it on the corresponding angle on the piece of paper exactly how they see it on the circle. In other words, if the distance is ABOVE the x-axis on the circle, put the spaghetti ABOVE the piece of yarn on the piece of legal sized paper. If it is BELOW, out the piece of spaghetti BELOW the string. Continue until you reach 2π (or 360°).
- Repeat steps 2 to 4, except instead of measuring the distance from the x-axis, measure it from the y-axis. If it is to the RIGHT of the y-axis, put the spaghetti ABOVE the string, and it is to the LEFT of the y-axis, put the spaghetti BELOW the string.