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Lesson Plan

Evaluate sine, cosine, and tangent functions using reference angles

teaches Common Core State Standards TR.UC.2
teaches Common Core State Standards TR.PF.7
teaches Common Core State Standards MAFS.912.F-TF.1.2
teaches Common Core State Standards CCSS.Math.Content.HSF-TF.A.2
teaches Common Core State Standards CCSS.Math.Practice.MP8
teaches Common Core State Standards CCSS.Math.Practice.MP4

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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. This lesson should be taught only after students are familiar with radians, the unit circle, and special triangles. At this point, students are making the connection that sine and cosine are represented on the unit circle as (cos t, sin t), and this will directly affect the sign of each of the functions in the different quadrants of the coordinate plane. Students will use that knowledge, along with a new concept (Reference Angles) to find the value of sine, cosine, and tangent of angles in the coordinate plane without a calculator. Vocabulary: Reference Angle Special Materials: Graph Paper
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