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Lesson Plan

Determine the domain of the trigonometric functions by using ratios

teaches Common Core State Standards CCSS.Math.Content.HSF-TF.A.2
teaches Common Core State Standards CCSS.Math.Practice.MP8
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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 exploration of the trigonometric functions and extends students' understanding to domain. The task allows students to use familiar ratios to look at division to determine when functions are defined and undefined. This builds toward the understanding of domain of the trigonometric functions and allows students to start to develop what the functions may look like. Vocabulary: domain, circular functions
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