Virginia flagVirginia: Trigonometry Math Standards

40 standards · 4 domains

CIRCULAR TRIGONOMETRY

  • 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.f Draw a reference right triangle when given the value of a trigonometric function of an angle (sine, cosine, tangent, cosecant, secant, and cotangent).
  • 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.1.j Calculate the area of a sector of a circle.
  • 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.

GRAPHS OF TRIGONOMETRIC FUNCTIONS

  • 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.GT.2.a Determine the domain and range of the inverse trigonometric functions.
  • T.GT.2.b Use the restrictions on the domain of an inverse trigonometric function to determine a value of the inverse trigonometric function.
  • T.GT.2.c Graph inverse trigonometric functions.

IDENTITIES AND EQUATIONS

  • T.IE.1.a Determine the values of trigonometric functions, with and without graphing technology.
  • T.IE.1.b Determine angle measures by using the inverse trigonometric functions, with and without a graphing technology.
  • T.IE.1.c Evaluate composite functions that involve trigonometric functions and inverse trigonometric functions.
  • 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.a.iv double-angle identities; and
  • T.IE.2.a.v half-angle 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.
  • T.IE.3.a Solve trigonometric equations with and without restricted domains algebraically and graphically.
  • T.IE.3.b Solve trigonometric inequalities algebraically and graphically.
  • T.IE.3.c Verify and justify algebraic solutions to trigonometric equations and inequalities, using graphing technology.

TRIANGLE TRIGONOMETRY

  • 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.TT.2.a Apply the Law of Sines, and the Law of Cosines, as appropriate, to find missing sides and angles in non-right triangles.
  • T.TT.2.b Recognize the ambiguous case when applying the Law of Sines and the potential for two triangle solutions in some situations.
  • T.TT.2.c Solve problems that integrate the use of the Law of Sines and the Law of Cosines and the triangle area formula (Area = 1/2 𝑎𝑏 sin 𝐶, where 𝑎 and 𝑏 are triangle sides and 𝐶 is the included angle) to find the area of any triangle, including those in contextual problems.