Chapter 15 - Trigonometric Functions
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"This chapter begins with a problem situation involving a Ferris wheel in which students explore how periodic functions are built. Lessons provide opportunities for students to analyze the graphs of periodic functions for characteristics such as the maximum, minimum, period, amplitude, and midline. Students will explore the unit circle to understand radian measure and convert between angle measures in degrees and radians. Using new understanding of the unit circle, radian measure, and periodic functions, students will investigate the sine and cosine functions as well as their characteristics and graphs. In the later part of the chapter, students recall the transformational function form g(x) = Af(B(x - C)) + D to graph and analyze transformations of the sine and cosine functions and build a graph of the tangent function using a context. Students will analyze the characteristics of the tangent graph, and apply their knowledge of transformations to sketch graphs of transformed tangent functions." Carnegie Textbook |
"Many flowers are able to follow the path of the Sun across the sky during the day. Young sunflowers exhibit this property—called phototropism. Once they are mature, though, sunflowers will usually face to the east all day long." - Carnegie Textbook
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Lesson 15.1 - Periodic Functions
"This lesson begins by asking students to build and analyze two different periodic functions that model the height of a person on a Ferris wheel as a function of the number of revolutions of the wheel. Students then build and analyze a similar function using angle measures as inputs." - Carnegie Textbook Lesson 15.2 - Radian Measure
"This lesson provides opportunities for students to analyze the unit circle and develop the radian as a unit of angle measure that is equal in magnitude to the corresponding intercepted arc length on a unit circle. " - Carnegie Textbook Lesson 15.3 - The Sine and Cosine Functions
"This lesson provides opportunities for students to synthesize their knowledge of the unit circle, radian measure, and the behavior of the graphs of periodic functions to build an understanding of the sine and cosine functions and their specific characteristics." - Carnegie Textbook Lesson 15.4 - Transformations of Sine and Cosine Functions
"The lesson provides opportunities for students to analyze transformations of sine and cosine functions individually. " - Carnegie Textbook Lesson 15.5 - The Tangent Function
"The lesson provides opportunities for students to build the graph of the tangent function, including the asymptotes, in context by modeling the change in the slope of a terminal ray as it traverses the unit circle in standard position." - Carnegie Textbook |
Reciprocal Functions
This additional lesson is not in the textbook. It will give students an opportunity to explore the characteristics of the reciprocal trigonometric functions: secant, cosecant, cotangent. Trigonometric Identities
This additional lesson is not in the textbook. It will give students an opportunity to learn about the three Pythagorean identities and how to use trig identities to simplify an expression. Trigonometric Equations
This additional lesson is not in the textbook. It will give students an opportunity to learn how to solve trigonometric equations using the unit circle and algebraic techniques. |
