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Course: Algebra II Unit of Study: Unit 7 -- Modeling with Trigonometric FunctionsBeginning Date: 12/10/12 Ending Date: 12/14/12State competency goal: F.TF.1 Know that if the length of an arc subtended by an angle is the same length as the radius of the circle, then the measure of the angle is 1 radian.F.TF.1 Know that the graph of the function, f, is the graph of the equation y=f(x).F.TF.2 Explain how radian measures of angles rotated counterclockwise in a unit circle are in a one-to-one correspondence with the non-negative real numbers, and that angles rotated clockwise in a unit circle are in a one-to-one correspondence with the non-positive real numbers.F.IF.2 When a relation is determined to be a function, use f(x) notation.F.IF.2 Evaluate functions for inputs in their domain.F.IF.2 Interpret statements that use function notation in terms of the context in which they are usedF.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.F.IF.7e Trigonometric functions, showing period, midline, and amplitude.DateBig Question (s):Activating Strategy/ Emotional Hook(1. Start the lesson)Teacher Input(2. Presentation)Student Active Participation(3. Guided practice)__________________________Additional Student Activities(4. Independent practice)Summarizing Activity(5. Evaluation)Closure________________________Homework 12/10/12How do I use exponential models to solve problems?Warm- ups:See attachedInstruction: Exponential functions and LogarithmsGuided Practice: Sorting Functions Activity(time permits)Independent Practice:Unit 5 testUnit 5 testExp., models, and operations w/ logs #23- 3412/10/12How do you convert angle measures between degrees and radians, find the area of a sector of a circle, and calculate the angular speed of an object?F.TF.2Warm- ups:See attached10-1: Defining the Circular FunctionsExamples A & BInstruction: 10-1: Defining the Circular Functions10-2: Radian Measure and Arc LengthGuided Practice:10-2: Radian Measure and Arc Length notes (pg. 4-5)Independent Practice:"Paddle Wheel" Investigation"A Circle of Radians" InvestigationTOD / Quiz 10-1 to 10-2 (?)Answer the EQLesson 10.2 ? Radian Measure and Arc Length12/11/12How do I determine if a function is even or odd?Warm- ups:See attachedInstruction: Even and Odd FunctionsGuided Practice: Even and Odd FunctionsIndependent Practice:Even and Odd Functions Unit 5 testCoterminal angles activity12/11/12Find equations for sinusoids● Identify the amplitude, period, and phase shift of a sinusoid● Model real data with a sinusoidal function● Find equations for transformations of the tangent functionF.TF.1Warm- ups:See attachedInstruction: 10-3: Graphing Trigonometric Functions/ 10-4: Inverses of Trigonometric FunctionsGuided Practice:10-3: Graphing Trigonometric Functions notes (pg. 6-8)10-4: Inverses of Trigonometric Functions notes (pg. 9-11)Independent Practice:Lesson 10.3 ? Graphing Trigonometric FunctionsTOD / Quiz 10-1 to 10-2Answer the EQLesson 10.4 ? Inverses of Trigonometric Functions12/12/12How do you interpret trigonometric equations that model real situations and write trigonometric equations to model real situations?2.04Warm- ups:See attachedInstruction: 10-5: Modeling with Trigonometric FunctionsGuided Practice: 10-5: Modeling with Trigonometric Functions notes (pg. 12-13)Independent Practice:"A Bouncing Spring"Investigation Quiz 10-3 to 10-4 TOD /Quiz 10-3 to 10-4Lesson 10.5 ? Modeling with Trigonometric Equations12/13/12How do you define the cotangent, secant, and cosecant functions, apply the reciprocal identities and use them to prove other trigonometricIdentities, and derive and prove three Pythagorean identities? 2.04Warm- ups:See attachedInstruction: 10-6:Fundamental Trigonometric Identities/ 10-7: Combining Trigonometric FunctionsGuided Practice: 10-6:Fundamental Trigonometric Identities notes (pg. 14-15)10-7: Combining Trigonometric Functions notes (pg. 16-17)Independent Practice:Lesson 10.6 ? Fundamental Trigonometric IdentitiesProblems from textLesson 10.6 ? Fundamental Trigonometric IdentitiesLesson 10.7 ? Combining Trigonometric Functions12/14/12How can you identify the relationship between circular motion and the sine and cosine functions?Warm- ups:See attachedInstruction: Trigonometric FunctionsGuided Practice: Review: Trigonometric FunctionsIndependent Practice:Assessment: Trigonometric FunctionsAssessment: Trigonometric FunctionsnoneLiteracy enhancements/Key Vocabulary:Sine , cosine, radian, period, function, amplitude, unit circle, trig identities, sum of two sinusoidal equations, cotangent, secant, cosecant, reciprocal identities, Pythagorean identities, frequencies, restricting the range, sinusoids, tangent function, phase shift, Model real data, arc lengths, area of a sector, angular speed, standard position, terminal side, circular functions, reference anglesAdaptations/Differentiation: MondayWarm- ups: Date:_____________Modeling Real-World Data: Curve Fitting pg. 539#1- 6Student textTuesday Warm- ups: Date:______________ WednesdayWarm- ups:Date:_____________1.??Change to degrees.??A.180° B.90° C.45°D.135°?2.??Name one positive angle and one negative angle that is co-terminal with -40°. ??A.–400°, 310°B.-180°, 320°C.–400°, 320°D.400°, -310°?3.??Choose the angle that measure.??A.B.C.D.???4.??What is the degree measure of the angle through which the hour hand on a clock rotates from 4:00 P.M. to 8:00 P.M.???A.90°B.120°C.–90°D.–120°?5.??How would the angle 130° be constructed???A.Draw the terminal side of the angle 50° counter-clockwise past the negative x-axis.B.Draw the terminal side of the angle 50° counter-clockwise past the positive x-axis.??C.Draw the terminal side of the angle 40° counter-clockwise past the positive y-axis.D.Draw the terminal side of the angle 40° counter-clockwise past the negative y-axis.ThursdayWarm- ups:Date:_____________1.??Find the exact value of sin θ, cos θ, and tan θ if the terminal side of θin standard position contains the point (5, 12).??A.sin , cos , tan B. sin , cos , tan C. sin , cos , tan D.sin , cos , tan ?2.??What is sin θ if θ is in standard position, its terminal side lays in quadrant IV and sec θ = 3 ? A. 22B.- 63C.- 33D.33?3.??What is the reference angle of 240°???A.60°B.120°C.–120° D.–60°?4.??For which trigonometric functions is an angle that measures 180° undefined???A.sec and tanB.csc and cotC.tan and cotD.csc and sec5.??Suppose Johnny was standing at the origin. Then, he walked northwest at an angle of 60° with respect to west. If the distance that he traveled is 16 units, what is his present position?FridayWarm- ups:Date:______________1. Rewrite (sin2 x + cos2 x) ÷ tan x as an expression involving only cot x. A.cot2xB. cot x C.2 cot xD.1 – cot x2. Which expression is equivalent to csc x – sin x?A.cos2x + sin2xB.sin x + cos x C.sin x – cos xD.cos2sinxx ................
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