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Wentzville School District Curriculum Development Template Stage 1 – Desired Results Unit 2 - Trigonometric Functions Unit Title: Trigonometric Functions Course: Math Analysis Brief Summary of Unit: In this unit students will use trigonometry to solve triangles. They will use various methods including right triangle rules, Law of Sines, and Law of Cosines. In addition, students will measure angles using both degree and radian measure. Students will extend trigonometric properties to angles that are greater than 90 degrees or less than zero degrees. Students will graph all six trigonometric functions and their inverses. Finally, students will model and solve real-world problems involving trigonometric functions. Textbook Correlation: Glencoe PreCalculus Chapter 4 Textbook Correlation: 4 weeks WSD Overarching Essential Question Students will consider… ● ● ● ● ● ● ● ● ● ● ● How do I use the language of math (i.e. symbols, words) to make sense of/solve a problem? How does the math I am learning in the classroom relate to the real-world? What does a good problem solver do? What should I do if I get stuck solving a problem? How do I effectively communicate about math with others in verbal form? In written form? How do I explain my thinking to others, in written form? In verbal form? How do I construct an effective (mathematical) argument? How reliable are predictions? Why are patterns important to discover, use, and generalize in math? How do I create a mathematical model? How do I decide which is the best mathematical tool to use to solve a problem? WSD Overarching Enduring Understandings Students will understand that… ● ● ● ● ● ● ● ● Mathematical skills and understandings are used to solve real-world problems. Problem solvers examine and critique arguments of others to determine validity. Mathematical models can be used to interpret and predict the behavior of real world phenomena. Recognizing the predictable patterns in mathematics allows the creation of functional relationships. Varieties of mathematical tools are used to analyze and solve problems and explore concepts. Estimating the answer to a problem helps predict and evaluate the reasonableness of a solution. Clear and precise notation and mathematical vocabulary enables effective communication and comprehension. Level of accuracy is determined based on the context/situation. ● ● ● How do I effectively represent quantities and relationships through mathematical notation? How accurate do I need to be? When is estimating the best solution to a problem? ● ● Using prior knowledge of mathematical ideas can help discover more efficient problem solving strategies. Concrete understandings in math lead to more abstract understanding of math. Transfer Students will be able to independently use their learning to… recognize periodic phenomena and understand that the situation can be modeled by trigonometric functions. Meaning Essential Questions Understandings Students will consider… Students will understand… ● ● ● ● ● How is trigonometry used to find unknown values? Why are certain values undefined for certain functions? How can you analyze the graphs of sine, cosine, tangent, cotangent, secant, and cosecant functions, and their inverses? When is it best to use radian measure? Degree measure? What types of real-world contexts can be modeled using trigonometric functions? ● ● ● ● The six trigonometric functions and their inverses can be used to solve problems even when the relationship does not involve a triangle. Radians are practical in real world situations. Relationships in triangles can be used to solve problems. Relationships and patterns in the real-world that are periodic can be modeled using trigonometric functions. Acquisition Acquisition Key Knowledge Key Skills Students will know… Students will be able to…. ● ● ● ● ● ● sine cosine tangent cotangent cosecant secant ● ● ● Convert degree measures to radian measure and vice versa Use radians to evaluate arc length, area of a sector, angular velocity, and linear velocity. Evaluate trig functions for all angle values ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● inverse sine (arcsine, Arcsine) inverse cosine (arccosine, Arccosine) inverse tangent (arctangent, Arctangent) radian measures reference angle periodic function amplitude frequency Law of Sines Law of Cosines ambiguous case phase shift period coterminal one to one arc length area of a sector angular velocity linear velocity ● ● ● ● ● ● ● Find values of trigonometric functions using the unit circle Graph all 6 trig functions with changes in amplitude and period, vertical translation and phase shift Model data using sinusoidal functions. Evaluate inverse trigonometric functions. Graph inverse trig functions (principal values only) Solve non-right triangles using the Law of Sines and Law of Cosines (including the ambiguous case) Solve real-world problems that involve trigonometry using multiple strategies. Standards Alignment MISSOURI LEARNING STANDARDS Extend the domain of trigonometric functions using the unit circle. F-TF-1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. F-TF-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. F-TF-3 (+) 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, cosine, and tangent for x, π + x, and 2π - x in terms of their values for x, where x is any real number. F-TF-4 (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. F-TF-5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.* F-TF-6 (+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. F-TF-7 (+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.* MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning. Show Me-Standards Goal 1: 1, 4, 5, 6, 7, 8 Goal 2: 2, 3, 7 Goal 3: 1, 2, 3, 4, 5, 6, 7, 8 Goal 4: 1, 4, 5, 6 Mathematics: 1, 4, 5