Spaghetti Trigonometry

Specific Expectations

2.3 make connections between the sine ratio and the sine function and between the cosine ratio and the cosine function by graphing the relationship between angles from 0º to 360º and the corresponding sine ratios or cosine ratios, defining this relationship as the function f(x) =sinx or f(x) =cosx, and explaining why the relationship is a function
2.4 sketch the graphs of f(x) =sinx and f(x) =cosx for angle measures expressed in degrees, and determine and describe their key properties

Materials

Spaghetti, yarn, paper, glue.

Important Terminology

Sine, Cosine, Unit Circle, cycle, domain, range, intercepts, amplitude, period, maximum and minimum values, increasing/decreasing intervals

Background Knowledge

An understanding of the definitions of the sine and cosine ratio.

Lesson Sequence

Follow lesson 1 of Spaghetti Trig, using angles in degrees instead of radians. Split the students into groups of 2 or 3, have half the students do sine and half cosine.

Key Questions

What is the relationship between the graph and the sine ratio? Is it a function? Why is it called a "unit circle", what are the cycle, domain, range, intercepts, amplitude, period, maximum and minimum values, increasing/decreasing intervals

Assessment

Formative: Have the students answer the key questions in their math journals

Enrichment

Those who are finishing early can add more angles to their project.

Remediation

Extra time can be given to students who need it. Since it's group work, you can match students with difficulties with students that can support them.

Implications for Future Lessons