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Unit Design Content Area Grade/Course Unit Title Duration of Unit Warren County Public Schools Mathematics HS Algebra 2 Unit 12: Trigonometry 8 days Priority Standards HSF.IF.C.7e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. HSF.IF.B.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* HSF.IF.B.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.* HSF.TF.B.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. HSF.TF.A.2: 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. Quality Core Standards G.3. Trigonometric and Periodic Functions A. Use the law of cosines and the law of sines to find the lengths of sides and measures of angles of triangles in mathematical and real-world problems. B. Use the unit-circle definition of the trigonometric functions and trigonometric relationships to find trigonometric values for general angles. C. Measure angles in standard position using degree or radian measure and convert a measure from one unit to the other. D. Graph the sine and cosine functions with and without technology. E. Determine the domain and range of the sine and cosine functions, given a graph. F. Find the period and amplitude of the sine and cosine functions, given a graph. G. Use sine, cosine, and tangent functions, including their domains and ranges, periodic nature, and graphs, to interpret and analyze relations. Supporting Standards HSF.BF.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Unit Design Warren County Public Schools Include recognizing even and odd functions from their graphs and algebraic expressions for them. HSF.TF.A.1: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. HSA.CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Concepts (nouns) Law of Sines and law of Cosinses Trigonometric Functions Key Features (Domain, Range, Amplitude, Period) Unit Circle Angle Measurements Skills (verbs) Apply Bloom’s Level (verb) Apply (3) Graph, model, evaluate Create (5) Interpret, relate Analyze (6) Use, find Convert Apply (3) Understand (2) Learning Targets LT1: Apply Law of Sines and Law of Cosines to find an unknown side or angle measure. (3) LT2: Convert angle measures from radians to degrees and vice versa. (2) LT3: Use the unit-circle definition of the trigonometric functions and trigonometric relationships to find trigonometric values for general angles. (3) LT4: Graph and interpret key features (such as amplitude, period, asymptotes, domain, range, graphs, etc.) of sine, cosine, and tangent functions. (6) Determine Big Ideas (lifelong understandings) Trigonometric functions can be used to model and analyze real world problems. Write Essential Questions (Answer Big Idea, hook student interest. There is a fire between two towers, which ranger can get to the fire the quickest? Formative Assessment Lesson(s): “The teacher leaders for the Gates grant work recommend that Warren County Administration adopt the practice that Warren County Math teachers do a minimum of one Formative Assessment Lesson per quarter. Other choices for formative assessment lessons may be found at http://map.mathshell.org/materials/lessons.php . Common Assessment(s): HS Algebra 2 Unit 12 DCA – Trigonometry Version A HS Algebra 2 Unit 12 DCA – Trigonometry Version B HS Algebra 2 Unit 12 DCA – Trigonometry Version C Note: HS Algebra 2 Unit 12 DCA – Trigonometry Review is to be used in conjunction with the above assessments.