Course 4 Unit 4 - Trigonometric Functions and Equations
Mathematics Course 2 Unit 6, Trigonometric Methods,
students learned right triangle trigonometry, the Law of Sines, and
the Law of Cosines. The sine and cosine function work was mainly
with angles measured in degrees in the first quadrant although some
tasks considered angles in other quadrants. In Course 3 Unit 6, Circles
and Circular Functions, the work with circular functions, sine,
cosine, and tangent functions was extended to all quadrants and radian
measure was introduced. In Unit 8, Inverse Functions,
students developed an understanding of the inverse functions for
the sine, cosine, and tangent and then used inverse trigonometric
functions to solve application problems. In Course 4 Unit 1,
students reviewed the sine and cosine functions in the context of
families of functions. (See the CPMP
Courses 1-4 descriptions.)
In this unit, students
review and extend their understanding of trigonometric functions. The
development emphasizes symbolic reasoning with equivalent expressions
in the contexts of identities and equations involving trigonometric functions.
Students manipulate the symbolic representations to obtain equivalent
representations that may be "simpler" or more easily interpreted, graphed,
or used. In addition, complex numbers are revisited and connected to
trigonometric functions, identities, and polar coordinates. A major goal
of this unit is to help students become proficient in symbolic reasoning,
rewriting trigonometric expressions into equivalent forms, and using
trigonometric relations to understand the geometry of complex numbers.
of the Unit
- Know and
be able to use the definitions of the six trigonometric functions
of an angle in standard position
and use the fundamental trigonometric identities
complex numbers geometrically
multiplication and division of complex numbers geometrically
- Use De Moivre's
Theorem to find powers and roots of complex numbers
The sample material
below is from Lesson 3, "The Geometry of Complex Numbers." This
second investigation draws on the process of multiplying complex numbers
developed in Investigation 1 to develop the connection between multiplication
of complex number expressed in trigonometric form and transformations
of the coordinate plane (De Moirvre's Theorem).
This content is recommended in the Common
Core State Standards (CCSS) for Mathematics for students planning
to concentrate in mathematics and science in postsecondary programs.
See: N-CN, #5 of the CCSS document.
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.
Unit Table of Contents and Sample Lesson Material
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