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Skills available for Virginia high school math standards

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Virginia Curriculum Framework: Algebra I Virginia Curriculum Framework: Algebra I
Virginia Curriculum Framework: Algebra II Virginia Curriculum Framework: Algebra II
Virginia Curriculum Framework: Algebra, Functions and Data Analysis Virginia Curriculum Framework: Algebra, Functions and Data Analysis
Virginia Curriculum Framework: Geometry Virginia Curriculum Framework: Geometry
Virginia Curriculum Framework: Mathematical Analysis Virginia Curriculum Framework: Mathematical Analysis
Virginia Curriculum Framework: Probability and Statistics Virginia Curriculum Framework: Probability and Statistics
Virginia Curriculum Framework: Trigonometry Virginia Curriculum Framework: Trigonometry
Virginia College and Career Ready Performance Expectations Virginia College and Career Ready Performance Expectations
Virginia Standards of Learning (2023): Algebra 1 Virginia Standards of Learning (2023): Algebra 1
Virginia Standards of Learning (2023): Algebra 2 Virginia Standards of Learning (2023): Algebra 2
Virginia Standards of Learning (2023): Algebra, Functions and Data Analysis Virginia Standards of Learning (2023): Algebra, Functions and Data Analysis
Virginia Standards of Learning (2023): Discrete Mathematics Virginia Standards of Learning (2023): Discrete Mathematics
Virginia Standards of Learning (2023): Geometry Virginia Standards of Learning (2023): Geometry
Virginia Standards of Learning (2023): Mathematical Analysis Virginia Standards of Learning (2023): Mathematical Analysis
Virginia Standards of Learning (2023): Probability and Statistics Virginia Standards of Learning (2023): Probability and Statistics
Virginia Standards of Learning (2023): Trigonometry Virginia Standards of Learning (2023): Trigonometry

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Triangular and Circular Trigonometric Functions

T.1 The student, given a point on the terminal side of an angle in standard position, or the value of the trigonometric function of the angle, will determine the sine, cosine, tangent, cotangent, secant, and cosecant of the angle.
- T.1.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
  - T.1.a.1 Define the six triangular trigonometric functions of an angle in a right triangle.
  - T.1.a.2 Draw a reference right triangle when given a point on the terminal side of the angle in standard position.
  - T.1.a.3 Draw a reference right triangle when given the value of a trigonometric function of the angle.
  - T.1.a.4 Determine the value of any trigonometric function when given a point on the terminal side of an angle in standard position.
  - T.1.a.5 Given one trigonometric function value, determine the other five trigonometric function values.
T.2 The student will develop and apply the properties of the unit circle in degrees and radians.
- T.2.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
  - T.2.a.1 Define the six circular trigonometric functions of an angle in standard position.
  - T.2.a.2 Apply the properties of the unit circle to determine trigonometric function values of special angles and their related angles in both degrees and radians without using a graphing utility.
  - T.2.a.3 Apply the properties of the unit circle to convert between special angles expressed in radians and degrees, without using a graphing utility.

Graphs of Trigonometric Functions

T.3 The student, given one of the six trigonometric functions in standard form, will a) state the domain and the range of the function; b) determine the amplitude, period, phase shift, vertical shift, and asymptotes; c) sketch the graph of the function by using transformations for at least a two-period interval; and d) investigate the effect of changing the parameters in a trigonometric function on the graph of the function.
- T.3.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
  - T.3.a.1 State the domain and the range of a trigonometric function written in standard form. (a)
  - T.3.a.2 Determine the amplitude, period, phase shift, vertical shift, and asymptotes of a trigonometric function from the equation of the function and from the graph of the function. (b)
  - T.3.a.3 Describe the effect of changing A, B, C, or ?? in the standard form of a trigonometric equation. (d)
  - T.3.a.4 Sketch the graph of a function written in standard form by using transformations for at least a two-period interval, including both positive and negative values for the domain. (c)
T.4 The student will graph the six inverse trigonometric functions.
- T.4.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
  - T.4.a.1 Determine the domain and range of the inverse trigonometric functions.
  - T.4.a.2 Use the restrictions on the domains of the inverse trigonometric functions in determining the values of the inverse trigonometric functions.
  - T.4.a.3 Graph inverse trigonometric functions.

Equations and Identities

T.5 The student will verify basic trigonometric identities and make substitutions, using the basic identities.
- T.5.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
  - T.5.a.1 Use trigonometric identities to make algebraic substitutions to simplify and verify trigonometric identities. The basic trigonometric identities include
    - T.5.a.1.1 reciprocal identities;
    - T.5.a.1.2 Pythagorean identities;
    - T.5.a.1.3 sum and difference identities;
      - Complementary angle identities (A2-MM.1)
      - Complementary angle identities (PC-T.1)
    - T.5.a.1.4 double-angle identities; and
    - T.5.a.1.5 half-angle identities.
T.6 The student will solve trigonometric equations and inequalities.
- T.6.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
  - T.6.a.1 Solve trigonometric equations with and without restricted domains algebraically and graphically.
  - T.6.a.2 Solve trigonometric inequalities algebraically and graphically.
  - T.6.a.3 Verify algebraic solutions, using a graphing utility.
T.7 The student will determine the value of any trigonometric function and inverse trigonometric function.
- T.7.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
  - T.7.a.1 Use a graphing utility to determine the trigonometric function values of any angle in either degrees or radians.
  - T.7.a.2 Define inverse trigonometric functions.
  - T.7.a.3 Determine angle measures by using the inverse trigonometric functions when the trigonometric function values are given.

Applications of Trigonometric Functions

T.8 The student will create and solve practical problems involving triangles.
- T.8.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
  - T.8.a.1 Create and solve practical problems involving triangles.
  - T.8.a.2 Use the trigonometric functions, Pythagorean Theorem, Law of Sines, and Law of Cosines to solve practical problems.
  - T.8.a.3 Use the trigonometric functions to model practical situations.
  - T.8.a.4 Identify a solution technique associated with triangles that could be used with a given problem.
  - T.8.a.5 Apply the sum and difference identities for sine, cosine, and tangent to solve problems.
T.9 The student will solve problems, including practical problems, involving a) arc length and area of sectors in circles using radians and degrees; and b) linear and angular velocity.
- T.9.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
  - T.9.a.1 Convert between any angle expressed in radians and degrees without using a graphing utility. (a)
    - Convert between radians and degrees (A2-II.1)
    - Convert between radians and degrees (PC-R.1)
  - T.9.a.2 Derive the relationship between the radian measure of an angle and the length of the intercepted arc. (a)
  - T.9.a.3 Calculate the length of an arc in radians. (a)
  - T.9.a.4 Calculate the area of sectors in circles. (a)
    - Area of sectors (G-W.7)
  - T.9.a.5 Solve practical problems involving linear and angular velocity. (b)

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Triangular and Circular Trigonometric Functions

T.1 The student, given a point on the terminal side of an angle in standard position, or the value of the trigonometric function of the angle, will determine the sine, cosine, tangent, cotangent, secant, and cosecant of the angle.

T.1.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

T.1.a.1 Define the six triangular trigonometric functions of an angle in a right triangle.

T.1.a.2 Draw a reference right triangle when given a point on the terminal side of the angle in standard position.

T.1.a.3 Draw a reference right triangle when given the value of a trigonometric function of the angle.

T.1.a.4 Determine the value of any trigonometric function when given a point on the terminal side of an angle in standard position.

T.1.a.5 Given one trigonometric function value, determine the other five trigonometric function values.

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

T.2.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

T.2.a.1 Define the six circular trigonometric functions of an angle in standard position.

T.2.a.2 Apply the properties of the unit circle to determine trigonometric function values of special angles and their related angles in both degrees and radians without using a graphing utility.

T.2.a.3 Apply the properties of the unit circle to convert between special angles expressed in radians and degrees, without using a graphing utility.

Graphs of Trigonometric Functions

T.3.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

T.3.a.1 State the domain and the range of a trigonometric function written in standard form. (a)

T.3.a.2 Determine the amplitude, period, phase shift, vertical shift, and asymptotes of a trigonometric function from the equation of the function and from the graph of the function. (b)

T.3.a.3 Describe the effect of changing A, B, C, or ?? in the standard form of a trigonometric equation. (d)

T.3.a.4 Sketch the graph of a function written in standard form by using transformations for at least a two-period interval, including both positive and negative values for the domain. (c)

T.4 The student will graph the six inverse trigonometric functions.

T.4.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

T.4.a.1 Determine the domain and range of the inverse trigonometric functions.

T.4.a.2 Use the restrictions on the domains of the inverse trigonometric functions in determining the values of the inverse trigonometric functions.

T.4.a.3 Graph inverse trigonometric functions.

Equations and Identities

T.5 The student will verify basic trigonometric identities and make substitutions, using the basic identities.

T.5.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

T.5.a.1 Use trigonometric identities to make algebraic substitutions to simplify and verify trigonometric identities. The basic trigonometric identities include

T.5.a.1.1 reciprocal identities;

T.5.a.1.2 Pythagorean identities;

T.5.a.1.3 sum and difference identities;

T.5.a.1.4 double-angle identities; and

T.5.a.1.5 half-angle identities.

T.6 The student will solve trigonometric equations and inequalities.

T.6.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

T.6.a.1 Solve trigonometric equations with and without restricted domains algebraically and graphically.

T.6.a.2 Solve trigonometric inequalities algebraically and graphically.

T.6.a.3 Verify algebraic solutions, using a graphing utility.

T.7 The student will determine the value of any trigonometric function and inverse trigonometric function.

T.7.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

T.7.a.1 Use a graphing utility to determine the trigonometric function values of any angle in either degrees or radians.

T.7.a.2 Define inverse trigonometric functions.

T.7.a.3 Determine angle measures by using the inverse trigonometric functions when the trigonometric function values are given.

Applications of Trigonometric Functions

T.8 The student will create and solve practical problems involving triangles.

T.8.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

T.8.a.1 Create and solve practical problems involving triangles.

T.8.a.2 Use the trigonometric functions, Pythagorean Theorem, Law of Sines, and Law of Cosines to solve practical problems.

T.8.a.3 Use the trigonometric functions to model practical situations.

T.8.a.4 Identify a solution technique associated with triangles that could be used with a given problem.

T.8.a.5 Apply the sum and difference identities for sine, cosine, and tangent to solve problems.

T.9 The student will solve problems, including practical problems, involving a) arc length and area of sectors in circles using radians and degrees; and b) linear and angular velocity.

T.9.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

T.9.a.1 Convert between any angle expressed in radians and degrees without using a graphing utility. (a)

T.9.a.2 Derive the relationship between the radian measure of an angle and the length of the intercepted arc. (a)

T.9.a.3 Calculate the length of an arc in radians. (a)

T.9.a.4 Calculate the area of sectors in circles. (a)

T.9.a.5 Solve practical problems involving linear and angular velocity. (b)