**Session Authors:** Mary Beth Richey and Mary Plumb

Developed as part of the Math Circles of Inquiry project, this five to six day activity is designed to help students understand trigonometric ratios, by building on their understanding of similar triangles and ratios of corresponding sides. The purpose of this module is for students to spend time and energy developing the reasons the sine, cosine and tangent ratios are effective tools for solving right triangles, by analyzing patterns that emerge when the trig table is compiled from class generated data, and to understand the numbers stored in their calculator before they start using it to problem solve.

An optional extension includes introducing the Unit Circle and the Pythagorean and Quotient Identities.

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Multiple representations**Topics:**

Geometry**Styles:**

Illustrates a concept, Multiple Related Problems**Mathematical Practices:**MP1, MP2, MP4, MP5, MP6, MP8