Verify and apply trigonometric identities.Construct the inverse of a trigonometric function, both graphically and algebraically when feasible.Inverse trigonometric functions, their properties and graphs.Discuss the scientific basis for radian measure.Analyze and interpret trigonometric functions using graphs, tables and equations.Demonstrate an understanding of the trigonometric functions as functions of real numbers.Trigonometric functions, their properties and graphs.Apply appropriate methods for solving quadratic equations, and discuss the advantages and disadvantages of each method.Describe the relationships among the discriminant, solutions of quadratic equations, and intercepts of parabolas.Choose and apply appropriate methods for solving systems of equations and inequalities, and describe the situation graphically where possible.Equations and Systems of Equations and Inequalities.Use the properties of exponential and logarithmic functions to solve equations, including equations which arise in applied settings.Discuss the historical and scientific basis for the logarithm.Recognize, use, and discuss the inter-relationships among roots of polynomial functions, factors of polynomials, and solutions of polynomial equations.Discuss the concept of inverses in a broad context and give examples. State and illustrate the fundamental properties of inverse functions.Use the algebra of functions and be able to relate it to the graphical representations.Deduce the possible shape of the graph from a given equation and vice-versa.Determine the major characteristics of graphs such as intercepts and asymptotes.
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