Search the California Content Standards

Cluster:
Define trigonometric ratios and solve problems involving right triangles.

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Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. *

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Define trigonometric ratios and solve problems involving right triangles.

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Derive and use the trigonometric ratios for special right triangles (30°, 60°, 90°and 45°, 45°, 90°). CA

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Apply trigonometry to general triangles.

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(+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

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Represent and solve equations and inequalities graphically. [Combine polynomial, rational, radical, absolute value, and exponential functions.]

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Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. *

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Understand solving equations as a process of reasoning and explain the reasoning. [Simple radical and rational]

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Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

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Interpret the structure of expressions. [Polynomial and rational]

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Interpret expressions that represent a quantity in terms of its context. * Interpret parts of an expression, such as terms, factors, and coefficients. *

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Interpret the structure of expressions. [Polynomial and rational]

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Interpret expressions that represent a quantity in terms of its context. * Interpret complicated expressions by viewing one or more of their parts as a single entity. *

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Interpret the structure of expressions. [Polynomial and rational]

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Use the structure of an expression to identify ways to rewrite it.

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Write expressions in equivalent forms to solve problems.

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Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.*

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Interpret functions that arise in applications in terms of the context. [Include rational, square root and cube root; emphasize selection of appropriate models.]

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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. *