PreCalculus - Course Standards
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StandardStandard TitleStandard Description
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5.1Radian and Degree MeasuresI can convert angle measures in radians to angle measures in degrees. In a circle, I can relate angles and arclengths to each other. I can solve modeling problems related to linear and angular measurements and their rates of change.
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5.2
Ratio Definitions for Trigonometric Functions
I can evaluate sine, cosine, tangent and their reciprocal functions in right triangles and at angles from the coordinate axes. I can relate values of these functions in one quadrant to those in other quadrants.
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5.3
Unit Circle Trigonometric Functions
I can evaluate the trigonometric functions and their reciprocal functions at given angles around the unit circle. I can apply definitions of these functions and knowledge of the unit circle to derive identities
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5.4
Inverse Trigonometric Functions
I can evaluate inverse trigonometric functions using knowledge of right triangles. I can evaluate compositions of trigonometric functions and their inverses.
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5.5
Graphs of Trigonometric Functions
I can relate graphs of the sine, cosine, and tangent functions to their equations. I can identify characteristics of these functions, including period, amplitude, axis intercepts, and phase shifts. I can identify the graphs of the reciprocal and inverse trigonometric functions.
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6.1
Modeling with Trigonometric Functions
I can write a sine or cosine function to model periodic phenomena. I can relate the period, frequency, amplitude, vertical shift, and phase of a given trigonometric function to describe a given physical situation.
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6.2Sum and Difference IdentitiesI can simplify expressions containing sines, cosines, or tangents of sums of angles using the identities. I can derive other angle identities using these formulas.
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6.3
Pythagorean and Multiple Angle Identities
I can apply half or double angle identities to simplify expressions containing trigonometric functions. I can use these identities to derive other identities.
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6.4
Solving Trigonometric Equations
I can use knowledge of the unit circle to solve equations stated in terms of trigonometric functions. I can find all solutions to an equation within a given interval.
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7.1Circles and EllipsesI can identify characteristics of circles and ellipses such as center, radius, vertices, and foci. I can relate algebraic, graphical, and verbal representations of circles and ellipses to each other.
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7.2HyperbolasI can identify characteristics of hyperbolas such as center, asymptotes, vertices, and foci. I can relate algebraic, graphical, and verbal representations of hyperbolas to each other.
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7.3ParabolasI can identify characteristics of parabolas, including vertex, directrix, and foci. I can relate algebraic, graphical, and verbal representations of parabolas to each other.
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8.1Counting PrinciplesI can use the counting principle to determine the number of possible outcomes of situations with and without repetition. This includes finding permutations and combinations of items.
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8.2Probabilities of Single EventsI can find probabilities of events using tree diagrams, Venn diagrams, and counting principles. I can find the probability of events involving the complement, unions, and intersections. I can make qualitative statements about the likelihood of an event.
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8.3
Compound Probability and Binomial Probability
I can calculate probabilities of multiple events that are either independent or not independent. I can calculate conditional probabilities. I can determine the probability of events with two outcomes occuring specific numbers of times.
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8.4Distributions of DataI can use tables or graphs of the distribution of a set of data to draw conclusions about the population. I can find probabilities of events involving distributions using technology, and calculate expected value for the distribution.
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