Academic Standards

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.

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.

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.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.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.

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

Correlation last revised: 11/18/2014

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.