Gizmos for Virginia - Mathematics: Trigonometry (Standards of Learning adopted 2023)

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

T.TT: : Triangle Trigonometry

T.TT.1: : The student will determine the sine, cosine, tangent, cotangent, secant, and cosecant of the acute angles in a right triangle and use these ratios to solve for missing sides and angle measures, including application in contextual problems.

T.TT.1.a: : Define and represent the six triangular trigonometric ratios (sine, cosine, tangent, cosecant, secant, and cotangent) of an angle in a right triangle.

T.TT.1.b: : Describe the relationships between side lengths in special right triangles (30°-60°-90° and 45°-45°-90°).

T.TT.1.c: : Use the trigonometric functions, the Pythagorean Theorem, the Law of Sines, and the Law of Cosines to solve contextual problems.

T.TT.1.d: : Represent and solve contextual problems involving right triangles, including problems involving angles of elevation and depression.

T.CT: : Circular Trigonometry

T.CT.1: : The student will determine the degree and radian measure of angles; sketch angles in standard position on a coordinate plane; and determine the sine, cosine, tangent, cosecant, secant, and cotangent of an angle, given a point on the terminal side of an angle in standard position or the value of a trigonometric function of the angle.

T.CT.1.a: : Define a radian as a unit of angle measure and determine the relationship between the radian measure of an angle and the length of the intercepted arc in a circle.

T.CT.1.b: : Determine the degree and radian measure of angles to include both negative and positive rotations in the coordinate plane.

T.CT.1.c: : Find both positive and negative coterminal angles for a given angle.

T.CT.1.d: : Identify the quadrant or axis in/on which the terminal side of an angle lies.

T.CT.1.e: : Draw a reference right triangle when given a point on the terminal side of an angle in standard position.

T.CT.1.g: : Determine the value of any trigonometric function (sine, cosine, tangent, cosecant, secant, and cotangent) when given a point on the terminal side of an angle in standard position.

T.CT.1.h: : Given one trigonometric function value, determine the other five trigonometric function values.

T.CT.1.i: : Calculate the length of an arc of a circle in radians.

T.CT.2: : The student will develop and apply the properties of the unit circle in degrees and radians.

T.CT.2.a: : Convert between radian and degree measure of special angles of the unit circle without the use of technology.

T.CT.2.b: : Define the six circular trigonometric functions of an angle in standard position on the unit circle.

T.CT.2.c: : Apply knowledge of right triangle trigonometry, special right triangles, and the properties of the unit circle to determine trigonometric functions values of special angles (0°, 30°, 45°, 60°, and 90°) and their related angles in degree and radians without the use of technology.

T.GT: : Graphs of Trigonometric Functions

T.GT.1: : The student will graph and analyze trigonometric functions and apply trigonometric functions to represent periodic phenomena.

T.GT.1.a: : Sketch the graph of the six parent trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) for at least a two-period interval.

T.GT.1.b: : Determine the domain and range, amplitude, period, and asymptote locations for a trigonometric function, given a graph or an equation.

T.GT.1.c: : Describe the effects of changing the parameters (A, B, C, or D in the standard form of a trigonometric equation) on the graph of the function using graphing technology.

T.GT.1.d: : Sketch the graph of a transformed sine, cosine, and tangent function written in standard form by using transformations for at least a two-period interval, including both positive and negative values for the domain.

T.GT.1.e: : Apply trigonometric functions and their graphs to represent periodic phenomena.

T.IE: : Identities and Equations

T.IE.1: : The student will evaluate expressions involving the six trigonometric functions and the inverse sine, cosine, and tangent functions.

T.IE.1.a: : Determine the values of trigonometric functions, with and without graphing technology.

T.IE.2: : The student will use basic trigonometric identity substitutions to simplify and verify trigonometric identities.

T.IE.2.a: : Use trigonometric identities to make algebraic substitutions to simplify and verify trigonometric identities. The basic trigonometric identities include:

T.IE.2.a.i: : reciprocal identities;

T.IE.2.a.ii: : Pythagorean identities;

T.IE.2.a.iii: : sum and difference identities;

T.IE.2.b: : Apply the sum, difference, and half-angle identities to evaluate trigonometric function values of angles that are not integer multiples of the special angles to solve problems, including contextual situations.

Correlation last revised: 4/9/2024

Virginia - Mathematics: Trigonometry

Standards of Learning | Adopted: 2023

T.TT: : Triangle Trigonometry

T.CT: : Circular Trigonometry

T.GT: : Graphs of Trigonometric Functions

T.IE: : Identities and Equations