Search the California Content Standards

Cluster:
Extend the domain of trigonometric functions using the unit circle.

Standard:
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

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Extend the domain of trigonometric functions using the unit circle.

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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.

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Extend the domain of trigonometric functions using the unit circle.

Standard:
Graph all 6 basic trigonometric functions. CA

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Model periodic phenomena with trigonometric functions.

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Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. *

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Translate between the geometric description and the equation for a conic section.

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Given a quadratic equation of the form ax^2 + by^2 + cx + dy + e = 0, use the method for completing the square to put the equation into standard form; identify whether the graph of the equation is a circle, ellipse, parabola, or hyperbola and graph the equation. [In Algebra II, this standard addresses only circles and parabolas.] CA

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Use probability to evaluate outcomes of decisions. [Include more complex situations.]

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(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). *

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Use probability to evaluate outcomes of decisions. [Include more complex situations.]

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(+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). *

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Calculate expected values and use them to solve problems.

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(+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. *

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Calculate expected values and use them to solve problems.

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(+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. *

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Calculate expected values and use them to solve problems.

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(+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.*