Unit 6: Trigonometric Functions & the Unit Circle

The big idea of this unit is trigonometric functions and the unit circle (F-TF.2).  In relation to this essential standard, students will need to understand radian measure (F-TF.1) and how the unit circle relates to the graph of trigonometric functions (CA F-TF.2.1).  As with most units, the connecting standards can also be reengaged with this new content with special attention to graphing functions, comparing functions, and equivalent forms of functions (F-IF.C) as well as key features and average rate of change (F-IF.B) while rewriting expressions will help students solve for the item in question (A-SSE.2).  One first choice in attempting to achieve depth in this unit might be to prove and use the Pythagorean Identity sin2(θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.  Another good choice for added depth may be to choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline if it was not already done as application in first instruction.  Other options, time permitting, include focusing on the details of interpreting expressions, explicit & recursive functions in context, and operations on functions.

Trigonometric functions are extended to all real numbers, and their graphs and properties are studied in this unit.  Based on their previous work with functions and their work with trigonometric ratios and circles in Geometry, students now use the coordinate plane to extend trigonometry to model periodic phenomena. 

Please note: the connecting standards in gray are essential standards, perhaps the most essential standards; they are not something previously covered and superfluous.  They are standards revisited throughout the course in new and different contexts.