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Ch13 and 14 Periodic Functions Cross-Curricular Ties: I Can… F.IF.7e F.TF.1 F.TF.2 F.TF.3* F.TF.5 F.BF.3 F.IF.8 Project ties: Derive the formula for the sum of a finite geometric series, and arithmetic series (when the common ratio is not 1), and use the formula to solve problems. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosines, and tangent for x, π + x, and 2π – x in terms of their values for x, where x is any real number. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline Add and subtract trigonometric functions and relate them to their graph. Explain different properties of the trigonmetric function Keywords: Amplitude Cotangent Period Cycle Radian Phase shift Unit circle Secant Sine and Cosine Function Topic(s) Step 1 2 3 4 5 6 7 8 Suggested Text PH2011 Common Core Exploring Periodic Data 13.1 F.IF.7e Angles and the Unit Circle 13.2 F.TF.1, F.TF.2, F.TF.3 Radian Measure 13.3 F.TF.1, F.TF.2, F.TF.3 The Sine Function 13.4 F.IF.7e F.TF.5 The Cosine Function 13.5 F.IF.7e F.TF.5 The Tangent Function 13.6 F.IF.7e Translating Sine and Cosine Functions 13.7 F.BF.3 Trigonometric Identities 14.1 F.IF.8 Trigonometric Identities 14.1 F.IF.8 Periodic motion graphs Activity 3x5 index cards Pg 711 example 1-4 Science, Technology, Engineering, & Math (STEM) Activities Assessment Periodic motion kahn Pg 713 1-25 odd Measuring reference angles notes Pg 718 examples 1,2, and 3 Pg 722 1-19 odd The unit circle notes Pg 721 example 4 and 5 Pg 722 21-49 odd Converting between Kahn radians and degrees Pg 726 example radians and degrees 1-4 9 10 11 12 13 14 15 16 17 18 19 20 Pg 729 1-27 odd (yes do number 13!) Reference triangles for the unit Tick to remembering the unit circle circle values FILL IN THE UNIT CIRCLE BELOW THIS UNIT GUIDE Where the trigonometric functions come from -Using the unit circle 0kahn intro to Pg 734 example 1-6 to generate graphs graphing trig functions Pg 734 example 1-4 -Graphing Sine 1Kahn drawing a sine Functions function -Sine and Cosine 2 kahn drawing out a Functions here cosine function (notes) 3 Amplitude and period of cosine and sine functions Pg 738 1-33 odd, pg746 1-21 odd Graphing tangent, What the tangent Pg 749 ex 1-3 cotangent, secant, and function looks like cosecant Pg 751 1-27 odd Step by Step of Pg 756 examples 1-5 Trigonometric Translating and functions shift graphing trigonometric functions Pg 760 1-35 odd http://www.youtube.com/watch?v=D3BykIrM6fk periodic love poem. Unit Circle Song All Students Take Calculus trick Pg 771 1-5, 7-35 odd Test http://www.youtube.com/watch?v=D3BykIrM6fk periodic love poem. : Prentice Hall Videos and Text Book http://phschool.com/webcodes10/index.cfm?area=view&wcprefix=auk&wcsuffix=0099 Chapter PowerPoints http://www.taosschools.org/ths/Departments/MathDept/quintana/GeometryPPTs/index.htm