TR.CO: Conics

TR.CO.1: Determine how the graph of a parabola changes if a, b and c changes in the equation y = a(x ? b)^2 + c. Find an equation for a parabola when given sufficient information.

Parabolas - Activity A
Parabolas - Activity B
Slope-Intercept Form of a Line - Activity B
Translating and Scaling Functions

TR.CO.2: Derive the equation of a parabola given a focus and directrix.

Parabolas - Activity A

TR.CO.3: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

Circles

TR.CO.4: Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

Ellipses - Activity A
Hyperbolas - Activity A
Parabolas - Activity A

TR.CO.5: Graph conic sections. Identify and describe features like center, vertex or vertices, focus or foci, directrix, axis of symmetry, major axis, minor axis, and eccentricity.

Circles
Hyperbolas - Activity A
Parabolas - Activity A
Parabolas - Activity B

TR.CO.6: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri?s principle, and informal limit arguments.

Circumference and Area of Circles
Prisms and Cylinders - Activity A

TR.UC: Unit circles

TR.UC.2: 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.

Cosine Function
Sine Function
Tangent Function
Unit Circle

TR.UC.3: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

Cosine Function
Sine Function
Tangent Function
Unit Circle

TR.G: Geometry

TR.G.1: Solve real-world problems with and without technology that can be modeled using right triangles, including problems that can be modeled using trigonometric ratios. Interpret the solutions and determine whether the solutions are reasonable.

Sine and Cosine Ratios - Activity A

TR.G.2: Explain and use the relationship between the sine and cosine of complementary angles.

Cosine Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine, and Tangent
Unit Circle

TR.G.3: Use special triangles to determine the values of sine, cosine, and tangent for π/3, π/4, and π/6. Apply special right triangles to the unit circle and use them to express the values of sine, cosine, and tangent for x, π + x, and 2π ? x in terms of their values for x, where x is any real number.

Cosine Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine, and Tangent
Tangent Function
Tangent Ratio
Unit Circle

TR.G.5: Understand and apply the Laws of Sines and Cosines to solve real-world and other mathematical problems involving right and non-right triangles.

Segment and Angle Bisectors

TR.PF: Periodic Functions

TR.PF.1: Find a sinusoidal function to model a data set and explain the parameters of the model.

Sine Function
Sine, Cosine, and Tangent

TR.PF.2: Graph trigonometric functions with and without technology. Use the graphs to model and analyze periodic phenomena, stating amplitude, period, frequency, phase shift, and midline (vertical shift).

Cosine Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine, and Tangent
Tangent Function
Tangent Ratio
Translating and Scaling Functions

TR.PF.3: Construct the inverse trigonometric functions of sine, cosine, and tangent by restricting the domain.

Sine Function
Sine, Cosine, and Tangent
Tangent Ratio

TR.PF.5: Prove the addition and subtraction formulas for sine, cosine, and tangent. Use the formulas to solve problems.

Cosine Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine, and Tangent
Sum and Difference Identities for Sine and Cosine
Tangent Function
Tangent Ratio
Unit Circle

TR.PF.6: Prove the double- and half-angle formulas for sine, cosine, and tangent. Use the formulas to solve problems.

Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine, and Tangent
Sum and Difference Identities for Sine and Cosine
Tangent Ratio
Unit Circle

TR.PF.7: Define and use the trigonometric ratios (sine, cosine, tangent, cotangent, secant, cosecant) in terms of angles of right triangles and the coordinates on the unit circle.

Cosine Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine, and Tangent
Tangent Function
Tangent Ratio
Unit Circle

TR.ID: Identities

TR.ID.1: Prove the Pythagorean identity sin^2(x) + cos^2(x) = 1 and use it to find trigonometric ratios, given sin(x), cos(x), or tan(x), and the quadrant of the angle.

Cosine Function
Simplifying Trigonometric Expressions
Sine Function
Sine, Cosine, and Tangent
Tangent Function
Tangent Ratio
Unit Circle

TR.ID.2: Verify basic trigonometric identities and simplify expressions using these and other trigonometric identities.

Simplifying Trigonometric Expressions

TR.PC: Polar Coordinates

TR.PC.1: Define polar coordinates and relate polar coordinates to Cartesian coordinates.

Points in Polar Coordinates

TR.PC.2: Translate equations from rectangular coordinates to polar coordinates and from polar coordinates to rectangular coordinates. Graph equations in the polar coordinate plane.

Points in Polar Coordinates