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Virginia Trigonometry Curriculum

Video lessons and practice for every Trigonometry topic. Aligned to Virginia Mathematics Standards of Learning so students are always on track.

Virginia Trigonometry Curriculum | StudyPugHelp

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ID

Standard

StudyPug Topic

CC.HSF.TF.A.1

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

CC.HSF.TF.A.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.

CC.HSF.TF.A.3

Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–x, π+x, and 2π–x in terms of their values for x, where x is any real number.

CC.HSF.TF.B.5

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

CC.HSF.TF.B.6

Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.

CC.HSF.TF.B.7

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.

CC.HSF.TF.C.8

Prove the Pythagorean identity sin^2(θ) + cos^2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.

CC.HSF.TF.C.9

Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

CC.HSG.CO.A.1

Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

CC.HSG.SRT.C.6

Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

CC.HSG.SRT.C.7

Explain and use the relationship between the sine and cosine of complementary angles.

CC.HSG.SRT.D.9

Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

CC.HSG.SRT.D.10

Prove the Laws of Sines and Cosines and use them to solve problems.

CC.HSG.SRT.D.11

Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.

CC.HSG.C.B.5

Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

Virginia Trigonometry: Key Topics and Standards

Virginia Trigonometry is a high school math course that deepens students' understanding of angles, functions, and geometric relationships. The course is aligned to Virginia's Mathematics Standards of Learning (SOL) and lays essential groundwork for Pre-Calculus and Calculus.

Unit Circle and Radian Measure

Students begin by understanding radian measure as the length of an arc on the unit circle subtended by an angle. The unit circle extends trigonometric functions beyond acute angles to all real numbers, interpreted as radian measures of angles traversed counterclockwise. Special triangles are used to find exact values of sine, cosine, and tangent for key angles such as π/6, π/4, and π/3.

Trigonometric Functions and Their Properties

Virginia Trigonometry students explore the symmetry and periodicity of sine, cosine, and tangent using the unit circle. They learn to identify even and odd functions and apply transformations to model periodic phenomena with specific amplitude, frequency, and midline.

  • Graphing and transforming sine and cosine functions
  • Choosing trig functions to model real-world periodic patterns
  • Understanding symmetry (odd/even) and period from the unit circle

Inverse Trigonometric Functions

By restricting the domain of a trigonometric function to an interval where it is always increasing or always decreasing, students learn how inverse functions are constructed. They then use inverse trig functions to solve equations that arise in applied modeling contexts, evaluating solutions with technology.

Trigonometric Identities

Students prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to find unknown trig values given a ratio and a quadrant. They also prove and apply addition and subtraction formulas for sine, cosine, and tangent to solve a variety of problems.

Right Triangle Trigonometry and Geometric Foundations

Building on precise definitions of geometric terms, students connect similarity to the idea that side ratios in right triangles depend only on the angles. This leads naturally to trigonometric ratios for acute angles, the relationship between sine and cosine of complementary angles, and the use of the Pythagorean Theorem in applied problems.

  • Defining trig ratios from angle similarity in right triangles
  • Solving applied right triangle problems using trig ratios
  • Using complementary angle relationships between sine and cosine

Laws of Sines and Cosines

Virginia Trigonometry students derive the area formula A = ½ab sin(C), prove the Laws of Sines and Cosines, and apply them to find unknown side lengths and angles in both right and non-right triangles. These tools are essential for solving real-world measurement problems.

Arc Length and Sector Area

Using similarity, students derive the fact that arc length is proportional to the radius, define radian measure as the constant of proportionality, and derive the formula for the area of a sector. These concepts connect geometry and trigonometry in a meaningful way.

StudyPug covers every one of these Virginia Trigonometry topics with video lessons and practice problems students can access anytime, on any device.