Course 4 Unit 7 - Functions and Symbolic Reasoning
1st Edition

In Course 4, the mathematical strands in the Contemporary Mathematics in Context program become increasingly blended within units. The content of this unit is from both the algebra and functions strand and the geometry and trigonometry strand. (See the descriptions of Course 4 Units.)

Unit Overview

Functions and Symbolic Reasoning extends student ability to manipulate symbolic representations of exponential, common and natural logarithmic, and trigonometric functions and to solve exponential, logarithmic, and trigonometric equations. Trigonometric identities are developed and proved or disproved. Geometric representations of complex numbers are used to reason about and to find roots of complex numbers.

Unit Objectives
  • To use properties of exponents to transform exponential expressions into equivalent exponential expressions
  • To solve exponential equations
  • To use relationships between logarithms and exponentials to write logarithmic equations in forms without logarithms
  • To know and be able to use the definitions of the six trigonometric functions of angles in standard position
  • To know and be able to use the fundamental trigonometric identities
  • To prove a statement of equality is an identity
  • To solve trigonometric equations
  • To represent complex numbers geometrically
  • To interpret multiplication of complex numbers geometrically
  • To use DeMoivre's Theorem to find all the roots of a complex number

Sample Overview

There are two different samples from Functions and Symbolic Reasoning. The first sample consists of Investigations 1 and 2 from Lesson 2, "Reasoning with Trigonometric Functions." These investigations introduce the cosecant, secant, and cotangent functions and begin work with trigonometric identities.

The second sample is the "Looking Back" lesson for this unit. This lesson is intended to provide students with tasks that will encourage them to look back at the unit as a whole. Students review, synthesize, and apply the knowledge gained during the study of the unit.

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 common pattern as elaborated under Instructional Design.

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How the Algebra and Functions Strand Continues

Algebraic representations of surfaces and conic sections are introduced in Unit 8, Space Geometry. A unit from the algebra and functions strand that develops understanding and skill in the use of standard spreadsheet operations while reviewing and extending many of the basic algebra topics from Courses 1-3 is recommended for students intending to pursue college programs in social, management, and some of the health sciences or humanities.

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