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.

Addition and Subtraction of Functions

Parabolas

Translating and Scaling Functions

Zap It! Game

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.

Circles

Distance Formula

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

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.

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

Ellipses

Hyperbolas

Parabolas

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

Pyramids and Cones

TR.UC.1: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

Sine Function

Tangent Function

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

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

Cosine Function

Sine Function

Tangent Function

Translating and Scaling Sine and Cosine Functions

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, Cosine, and Tangent Ratios

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

Sum and Difference Identities for Sine and Cosine

Tangent Function

Translating and Scaling Sine and Cosine Functions

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

Tangent Function

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

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

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

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, Cosine, and Tangent Ratios

Tangent Function

Translating and Scaling Sine and Cosine Functions

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.

Simplifying Trigonometric Expressions

Sine, Cosine, and Tangent Ratios

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

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

TR.V.1: Solve problems involving velocity and other quantities that can be represented by vectors.

TR.V.2: Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).

TR.V.3: Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).

Correlation last revised: 9/16/2020

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