teachersedition_ch07_pc3.pdf - 7 CHAP TE R O B J EC TIV E S \u2022 Investigate the sum of the squares of the cosine and sine of the same argument

# teachersedition_ch07_pc3.pdf - 7 CHAP TE R O B J EC TIV E S...

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Th e Foucault pendulum shown in the photograph provided physical proof in the middle of the 19th century that Earth is rotating about its axis. Pendulums can have many different paths in different planes. A pendulum’s path is a two- dimensional curve that you can describe by x - and y -displacements from its rest position as functions of time. You can predict a pendulum’s position at any given time using parametric equations. Pythagorean properties of trigonometric functions can be used to model periodic relationships and allow you to conclude whether the path of a pendulum is an ellipse or a circle. Trigonometric Function Properties and Identities, and Parametric Functions y x 1 343 Investigate the sum of the squares of the cosine and sine of the same argument. Derive algebraically three kinds of properties expressing relationships among trigonometric functions. Given a trigonometric expression, transform it into an equivalent expression whose form is perhaps simpler or more useful. Find algebraically or numerically the solutions to equations involving circular or trigonometric sines, cosines, and tangents of one argument. Given equations for a parametric function, plot the graph and make conclusions about the geometric figure that results. Plot graphs of inverse trigonometric functions and relations. Find exact values of inverse trigonometric functions. CHAPTER OBJECTIVES
Overview Here students broaden their repertoire of trigonometric properties, adding to the Pythagorean and quotient properties they learned in Chapter 5. In some cases they are asked to transform an expression to another form, and at other times they are asked to prove that a given equation is an identity. Students reinforce the proof style they learned in geometry, starting with “Proof:” to show where statement of the identity ends and proving begins, and ending with a statement of what they have proved, including the abbreviation “q.e.d.” The properties are also used to solve equations, adding arcsine and arctangent to the arccosine learned in Chapter 6. Students also learn to use parametric functions to plot the inverse circular relation graphs. Using This Chapter Th is chapter falls into the middle of Unit 2. Although some newer textbooks do not cover topics such as transforming trigonometric expressions and proving trigonometric identities, there are several reasons to include them. These concepts help students learn elementary trigonometric properties, give students an opportunity to sharpen their algebraic skills, and show students how to write algebraic proofs. Teaching Resources Explorations Exploration 7-2: Properties of Trigonometric Functions Exploration 7-3a: Transforming an Expression Exploration 7-3b: Trigonometric Transformations Exploration 7-3c: Trigonometric Identities Exploration 7-4a: Arccosine, Arcsine, and Arctangent Exploration 7-4b: Trigonometric Equations Exploration 7-5: Parametric Function Pendulum Problem Exploration 7-5a: Parametric Equations for Ellipses

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