• Understand that radian measure of an angle as the length of the arc on the unit circle that is subtended by the angle

• Relationship between degrees and radians.

• The unit circle is a circle with radius of length 1 centered at the origin.

• Find the measure of the angle given the length of the arc.

• Find the length of an arc given the measure of the central angle.

• Convert between radians and degrees.

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• Use the unit circle to evaluate sine, cosine and tangent of standard reference angles.

• Identify, label and be able to use a unit circle to solve problems.

• Define an angle in standard form as an angle drawn on a plane that has its vertex at the origin and its initial side along the positive x-axis.

• Define the sine, cosine, tangent, cosecant, secant and cotangent functions using the unit circle.

• Identify the domain and range of the trigonometric functions based on their definitions in terms of the unit circle.

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• Relationship between the unit circle in the coordinate plane and graph of trigonometric functions.

• Graph trigonometric functions, showing period, midline, and amplitude.

• Key features of a graph or table may include intercepts; intervals in which the function is increasing, decreasing or constant; intervals in which the function is positive, negative or zero; symmetry; maxima; minima; and end behavior.

• Given a verbal description of a relationship that can be modeled by a function, a table or graph can be constructed and used to interpret key features of that function.

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• Use characteristics of real world phenomena to select a trigonometric model.

• Identify amplitude, frequency and midline appropriate for the model.

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• Prove the Pythagorean identity: sin2(θ) + cos2(θ) = 1.

• Use the Pythagorean identity to find sin(θ), cos(θ), or tan(θ) when given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.

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• Fit exponential and trigonometric functions to data using technology.

• Solve problems using functions fitted to data (prediction equations).

• Interpret the intercepts of models in context.

• Plot residuals of non-linear functions.

• Analyze residuals in order to informally evaluate the fit of exponential and trigonometric functions.

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• Compare key attributes of functions each represented in a different way (i.e. zeros, end behavior, periodicity, asymptotes).

• A function can be represented algebraically, graphically, numerically in tables, or by verbal descriptions.

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• Functions of various types can be combined to model real world situations.

• Use arithmetic operations to combine functions of varying types in order to model relationships between quantities.

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• Function notation representation of transformations

• Perform transformations on graphs of polynomial, exponential, logarithmic, or trigonometric functions.

• Identify the effect on the graph of replacing f(x) by: 1) f(x) + k; 2) k f(x); 3) f(kx); 4) and f(x + k) for specific values of k (both positive and negative).

• Identify the effect on the graph of combinations of transformations.

• Given the graph, find the value of k.

• Illustrate an explanation of the effects on polynomial, exponential, logarithmic, or trigonometric graphs using technology.

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• For a function f(x) that has an inverse, the domain/input for f(x) is the inverse function’s range/output and that the range/output for f(x) is the inverse function’s domain/input.

• Use function notation to represent the inverse of a function (f-1(x)).

• Transform an equation in order to isolate the independent variable, recognizing that the domain/input for f(x) is the inverse function’s range/output and that the range/output for f(x) is the inverse function’s domain/input.