Lesson Plan

Discover and derive other Pythagorean identities by analyzing special right triangles constructed around the unit circle

teaches Common Core State Standards CCSS.Math.Content.HSF-TF.C.8 http://corestandards.org/Math/Content/HSF/TF/C/8
teaches Common Core State Standards CCSS.Math.Content.HSG-SRT.C.8 http://corestandards.org/Math/Content/HSG/SRT/C/8
teaches Common Core State Standards CCSS.Math.Practice.MP8 http://corestandards.org/Math/Practice/MP8

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Big Ideas: The Pythagorean identity, sin^2(x) + cos^2(x)=1, can be proved through analysis of a right triangle constructed inside the unit circle, and it can be used to solve problems involving unknown trigonometric function values. Other Pythagorean identities can be proved through analyzing carefully constructed right triangles in the unit circle, and they can be used to solve problems and simplify expressions. In this task, students are presented with a diagram that includes the familiar first quadrant reference triangle in addition to other right triangles formed by the x- and y-axes and a tangent line to the circle. Students will analyze the diagram to isolate the right triangles that contain a side length of 1 and show they are similar to the original reference triangle. From there, they will derive two more Pythagorean identities. This task and lesson should follow a lesson on discovering and using the first Pythagorean identity, but before lessons on any other more complex trigonometric identities. Vocabulary: trigonometric identity, Pythagorean Theorem Special Materials: none
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