### Course 2 Unit 7 - Trigonometric Methods ©2008

Trigonometry or "measure of triangles" is an important and useful area of mathematics that naturally connects concepts and methods of geometry and algebra. Trigonometric Methods builds on the Course 1 geometry unit, Patterns in Shape, and the Course 2 unit, Coordinate Methods. In Course 1, students explored the rigidity of triangles and minimal conditions that are sufficient to completely determine a triangle's size and shape. Once a triangle is completely determined, a next logical question is "How can the measures of the triangle's unknown, but rigidly determined, sides and angles be calculated?". Trigonometry provides those methods, namely, trigonometric ratios for right triangles and the Law of Sines and Law of Cosines for any triangle.

Unit Overview
In this unit, students develop the ability to use right triangle trigonometry to solve triangulation and indirect measurement problems. The also begin to develop an understanding of trigonometric functions.

 Objectives of the Unit Explore the sine, cosine, and tangent functions defined in terms of a point on the terminal side of an angle in standard position in a coordinate plane Explore properties and applications of the sine, cosine, and tangent ratios of acute angles in right triangles Determine measures of sides and angles for nonright triangles using the Law of Sines and Law of Cosines Use the Law of Sines and Law of Cosines to solve a variety of applied problems that involve triangulation Describe the conditions under which two, one, or no triangles are determined given the lengths of two sides and the measure of an angle not included between the two sides

Sample Overview
The sample student material below is from Lesson 2, "Using Trigonometry in Any Triangle." Students prove and use the Law of Sines in this investigation. Embedded in this work is solving proportions.

Instructional Design
Throughout the curriculum, interesting problem contexts serve as the foundation for instruction. As lessons unfold around these problem situations, classroom instruction tends to follow a four-phase cycle of classroom activities—Launch, Explore, Share and Summarize, and Apply. This instructional model is elaborated under Instructional Design.