Unit 1: Functions, Inverses and Their Graphs Learning Objectives Content Outline Skills and Concepts Instructional Materials Standards for Mathematical Practice 1a. Analyze and relate attributes of functions graphically, symbolically and in context. 1b.Connect selected parent functions to their transformations symbolically and graphically. CCSS: Analyze and relate attributes of functions graphically, symbolically, and in context. Construct selected parent function graphs and interpret transformations Apply function transformations to their graphs and their equations Apply concept of symmetry to selected functions Analyze and interpret intervals where functions are increasing and decreasing and representations in context [Stewart] Section 2.4 Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with math. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.
2.Recognize interpret and model inverse of selected functions algebraically, graphically and in context of real world examples CCSS: concept of graphical symmetry to functions and their inverses. Construct an inverse given a function and interpret results Analyze properties of inverse functions and verify if a function exists or if it is a one to one function [Stewart] Section 2.8 1 Make sense of problems and persevere in solving them. 2 Reason abstractly and quantitatively. 3 Construct viable arguments and critique the reasoning of others. Model with math. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. 3.Explore and interpret composition of functions and its effect on the domain and range of the newly composed function. CCSS: Formulate the composition of two functions. Investigate the restrictions on domain when a function input is restricted by another function Apply algebraic reasoning of compositions to the composition of a function and its inverse in determining if the function is one to one. Connect and analyze the impact the composing functions that has a domain restriction that continues to impact the newly composed function, including composing inverse functions. [Stewart] Section 2.7 Make sense of problems and persevere in solving them . Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with math. Use appropriate tools strategically Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.
5. Represent and interpret the measurement of radians to the radius of each circle encompassing the circumference 2π. CCSS: F.TF.A.1 F.TF.A.2 Apply radian measure to the fractional arc of a circle and equate it the central angle it intercepts, and rotations completed Analyze the relationship between degree and radians and use either measurement in context. Create a proportion to evaluate radians and degrees. Distinguish radian measure from degree measure of angles and explain conceptual understanding of radian measure (relationship to circumference of a unit circle). Convert between degree and radian measure. Interpret a positive and negative angle in standard position and connect the concept of coterminal angles and rotation counterclockwise or clockwise respectively. Find arc length and sector areas Derive the formulas for the arc length and sector area when using an angle in radian measure. [Stewart] Section 6.1 (Angle Measure) Make sense of problems and persevere in solving them . Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with math. Use appropriate tools strategically Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.
9a.Investigate and connect the concept of inverse functions as it relates to trigonometric functions. 9b. Analyze and evaluate inverse trigonometric functions. 9c. Explore and analyze compositions of trigonometric functions and inverse trigonometric functions. CCSS: F.TF.B.7 Construct the inverse applying properties of functions to restrict its domain and range. Connect domain and range restrictions in order to evaluate inverse of the sine, cosine, and tangent. Apply reciprocals function to analyze and evaluate inverse cosecant, secant, and cotangent. Explore the use of inverse trigonometric functions on the calculator to evaluate simple trigonometric equations that do not involve special angle measures or special side ratios. [Stewart] Section 7.4 (Inverse Trigonometric Functions) Make sense of problems and persevere in solving them . Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with math. Use appropriate tools strategically Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Unit 4 : Analytic Trigonometry and Applications of Trigonometric Functions Learning Objectives Content Outline Key Definitions, Skills and Concepts Instructional Materials Standards for Mathematical Practice
11.Integrate the study of trigonometry and the unit circle to find all solutions to trigonometric equations CCSS: F.TF.B.7 Isolate a trigonometric function by applying algebraic skills and integrating the concept of a periodic function to find all solutions to an equation. Connect and recognize when a trigonometric equation has a quadratic form and link with knowledge of solving quadratics. Formulate solutions to trigonometric equations when using inverse trigonometric functions and incorporate all solutions as it rotates around the unit circle. [Stewart] Section 7.5 (Trigonometric Equations) Make sense of problems and persevere in solving them . Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with math. Use appropriate tools strategically Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.