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Lesson Plan

Describe the features of the graphs of sine and cosine by using the unit circle

teaches Common Core State Standards CCSS.Math.Content.HSF-TF.A.2
teaches Common Core State Standards CCSS.Math.Practice.MP4
teaches Common Core State Standards CCSS.Math.Practice.MP6
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Big Ideas: The unit circle has a radius of 1, so sin (t) =y/1=y and cos(t) =x/1=x and any point on the unit circle (x, y) can be labeled (cos(t),sin(t)). Therefore cos(t) and sin(t) can be evaluated using the reference triangles derived from Pythagorean Theorem. A trigonometric ratio is a function that has a domain and can be graphed using the terminal ray of the unit circle. The sine and cosine functions have a period of 2pi and an amplitude of 1. The tangent graph is undefined at positive or negative pi/2 and has a period of pi . This lesson builds on the domain of the trig functions and allows students to see what the functions look like and what the features of each function are. The task pushes students to use their knowledge of the values of sine and cosine to develop a graph and discover its features. This builds toward more application problems of the periodic functions that will come in later lessons. Vocabulary: amplitude, period Special Materials: Graph Paper
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