Posted: Tue, 07/03/2018 - 2:12pm Updated: Fri, 08/03/2018 - 1:49pm

This Teacher Resource Guide has been developed to provide supporting materials to help educators successfully implement the Indiana Academic Standards for Trigonometry. These resources are provided to help you in your work to ensure all students meet the rigorous learning expectations set by the Indiana Academic Standards. Use of these resources are optional; teachers should decide which resources will work best in their classroom for their students.

The resources on this webpage are for illustrative purposes only, to promote a base of clarity and common understanding. Each item illustrates a standard but please note that the resources are not intended to limit interpretation or classroom applications of the standards.

The links compiled and posted on this webpage have been provided by classroom teachers, the Department of Education, and other sources. The IDOE has not attempted to evaluate any posted materials. They are offered as samples for your reference only and are not intended to represent the best or only approach to any particular issue. The IDOE does not control or guarantee the accuracy, relevance, timeliness, or completeness of information contained on a linked website; does not endorse the views expressed or services offered by the sponsor of a linked website; and cannot authorize the use of copyrighted materials contained in linked websites. Users must request such authorization from the sponsor of the linked website.

CONICS

Activities, Examples, or Resources

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.

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.

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.

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.

Area of a Circle

Circumference of a Circle

Volume Formulas for Cylinders and Prisms

Volume of a Special Pyramid

Use Cavalieri’s Principle to Compare Aquarium Volumes

UNIT CIRLCES

Activities, Examples, or Resources

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

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.

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

GEOMETRY

Activities, Examples, or Resources

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.

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

Sine and Cosine of Complementary Angles

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.

TR.G.4: Prove the Laws of Sines and Cosines and use them to solve problems.

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.G.6: Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line.  Use the formula to find areas of triangles.

PERIODIC FUNCTIONS

Activities, Examples, or Resources

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

Sinusoids:  Applications and Modeling

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).

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

Inverse Trigonometric Function Graphs

TR.PF.4: Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.

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

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

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.

IDENTITIES

Activities, Examples, or Resources

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.

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

POLAR COORDINATES

Activities, Examples, or Resources

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.

VECTORS

Activities, Examples, or Resources

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).