Lesson Plan

Simplify trigonometric functions and expressions by substituting equivalent values derived from the Pythagorean identities

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: 1. 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. 2. 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 trigonometric functions that appear on their surface to be quite complicated. They are instructed to graph the functions using technology and analyze the graphs. Students will see that the functions may not be as nearly as complicated as they originally thought, because the graphs resemble simple, familiar functions. They will then show through algebraic manipulation that the functions from the task can be simplified using substitution of the Pythagorean identities. This task should follow lessons on the Pythagorean identities, and serves to add wonder and intrigue into the trigonometric identities and as a primer to topics in Pre-Calculus. Special Materials: Students will require the use of graphing technology. This can be graphing calculators or tablets/computer with access to graphing software such as Desmos or GeoGebra.
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