Prove and apply the addition and subtraction formulas for sine, cosine, and tangent, and use them to derive and apply the double angle formulas.

Identify symmetry, end behavior, and periodicity from graphs; interpret key features from tables; and sketch graphs from verbal descriptions.

Convert between quadratic forms to optimize graphing, use graphing technology, and recognize constant, identity, and simple polynomial functions.

Analyze and graph rational functions by identifying asymptotes, holes, zeros, and end behavior, culminating in mixed practice with both function types.

Understand the key features of polynomial functions, including zeros, multiplicity, and end behavior, to prepare for graphing.

Identify transformations from equations and graphs, and recognize and verify even and odd functions graphically and algebraically.

Learners will solve real-world problems involving angles of elevation and depression, and decide when to use the Pythagorean Theorem versus trigonometric ratios.

Apply the Law of Sines and the Law of Cosines to solve real-world measurement problems involving surveying, navigation, and resultant forces.

Learners will use congruence and similarity criteria to solve for unknowns, prove segment and angle relationships, construct similar triangles, and tackle mixed proof problems in complex figures.

Calculate volumes of cylinders, pyramids, cones, spheres, and composite solids, and solve real-world volume problems.

Derive and apply formulas for arc length and sector area, and understand radian measure as the constant of proportionality between arc length and radius.

Learners will derive the area formula A = ½ab sin(C) and the Law of Sines, then use them to solve triangles in the AAS, ASA, and SSA cases, including the ambiguous case.

Write explicit and recursive formulas for arithmetic and geometric sequences, convert between forms, and use sequences to model real-world situations.

Identify and graph individual and combined transformations of function graphs, including shifts, stretches, and reflections.

Write functions that describe relationships between quantities from verbal descriptions, determining both explicit expressions and recursive processes.

Calculate average rate of change from tables, equations, and graphs; estimate instantaneous rate of change; and interpret rates of change in real-world contexts.

Construct inscribed, circumscribed, and tangent circles, and prove and apply properties of cyclic quadrilaterals in multi-step problems.

Identify and classify linear and exponential growth patterns by analyzing tables, graphs, verbal descriptions, and equations.

Combine functions using arithmetic operations and compose functions to model real-world situations where quantities depend on one another.

Compare properties and rates of change of functions given in different representations, including algebraic, graphical, tabular, and verbal forms.

Compare the long-term growth rates of linear, quadratic, and exponential functions using graphs, tables, and equations.