Trigonometry FlexBook® for Middle School

Trigonometry FlexBook® for High School

For Middle School

For High School

Levels are CK-12's student achievement levels.

Basic
Students matched to this level have a partial mastery of prerequisite knowledge and skills fundamental for proficient work.

At Grade (Proficient)
Students matched to this level have demonstrated competency over challenging subject matter, including subject matter knowledge, application of such knowledge to real-world situations, and analytical skills appropriate to subject matter.

Advanced
Students matched to this level are ready for material that requires superior performance and mastery.

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- Lengths of Triangle Sides Using the Pythagorean Theorem
- Identifying Sets of Pythagorean Triples
- Pythagorean Theorem to Classify Triangles
- Pythagorean Theorem to Determine Distance
- Classifications of Special Right Triangles
- Lengths of Sides in Isosceles Right Triangles
- Relationships of Sides in 30-60-90 Right Triangles
- Special Triangle Ratios
- Basic Trigonometric Functions
- Sine, Cosine, and Tangent Functions
- Secant, Cosecant, and Cotangent Functions
- Pythagorean Theorem for Solving Right Triangles
- Angles of Elevation and Depression
- Right Triangles, Bearings, and other Applications
- Measuring Rotation
- Angles of Rotation in Standard Positions
- Coterminal Angles
- Trigonometric Functions and Angles of Rotation
- Unit Circle
- Trigonometric Functions of Any Angle
- Reference Angles and Angles in the Unit Circle
- Trigonometric Functions of Negative Angles
- Trigonometric Functions of Angles Greater than 360 Degrees
- Reciprocal Identities
- Domain, Range, and Signs of Trigonometric Functions
- Quotient Identities
- Cofunction Identities and Reflection
- Pythagorean Identities

- Radian Measure
- Conversion between Degrees and Radians
- Six Trigonometric Functions and Radians
- Rotations in Radians
- Length of an Arc
- Area of a Sector
- Length of a Chord
- Angular Velocity
- Sine and Cosecant Graphs
- Sine Graph and Cosine Graph
- Cosine and Secant Graphs
- Tangent and Cotangent Graphs
- Secant Graph and Cosecant Graph
- Translating Sine and Cosine Functions
- Vertical Translations
- Horizontal Translations or Phase Shifts
- Amplitude
- Period
- Period and Frequency
- Amplitude and Period
- General Sinusoidal Graphs
- Graphing Tangent, Cotangent, Secant and Cosecant
- Tangent Graphs

- Trigonometric Identities and Equations
- Fundamental Trigonometric Identities
- Trig Identities to Find Exact Trigonometric Values
- Pythagorean Identity
- Even and Odd Identities
- Cofunction Identities
- Proofs of Trigonometric Identities
- Solving Trigonometric Equations
- Simplifying Trigonometric Expressions
- Simpler Form of Trigonometric Equations
- Trigonometric Equations Using Factoring
- Trigonometric Equations Using the Quadratic Formula
- Solving Trigonometric Equations Using Basic Algebra
- Sum and Difference Identities
- Solving Trigonometric Equations using Sum and Difference Formulas
- Cosine Sum and Difference Formulas
- Sine Sum and Difference Formulas
- Tangent Sum and Difference Formulas
- Finding Exact Trigonometric Values Using Sum and Difference Formulas
- Applications of Sum and Difference Formulas
- Simplifying Trigonometric Expressions using Sum and Difference Formulas
- Double Angle Identities
- Simplifying Trigonometric Expressions with Double-Angle Identities
- Solving Equations with Double-Angle Identities
- Finding Exact Trigonometric Values Using Double Angle Identities
- Half Angle Formulas
- Trigonometric Equations Using Half Angle Formulas
- Sum to Product Formulas for Sine and Cosine
- Product to Sum Formulas for Sine and Cosine
- Linear Combinations
- Triple-Angle Formulas and Linear Combinations

- Inverse Trigonometric Functions
- Basic Inverse Trigonometric Functions
- Definition of the Inverse of Trigonometric Ratios
- Exact Values for Inverse Sine, Cosine, and Tangent
- Inverse of Functions through Algebraic Manipulation
- Graphing Inverse Trigonometric Functions
- Inverses by Mapping
- Inverses of Trigonometric Functions
- Composition of Trig Functions and Their Inverses
- Definition of Inverse Reciprocal Trig Functions
- Composition of Inverse Reciprocal Trig Functions
- Trigonometry in Terms of Algebra
- Applications of Inverse Trigonometric Functions

- Triangles and Vectors
- Law of Cosines
- Derive the Law of Cosines
- Sides of an Oblique Triangle
- Determination of Unknown Angles Using Law of Cosines
- Identify Accurate Drawings of Triangles
- Alternate Formula for the Area of a Triangle
- Derivation of the Triangle Area Formula
- Heron's Formula
- Determination of Unknown Triangle Measures Given Area
- Law of Sines
- Angle-Angle-Side Triangles
- Angle-Side-Angle Triangles
- Solving Triangles Using the Law of Sines
- Ambiguous Case
- Possible Triangles with Side-Side-Angle
- General Solutions of Triangles
- Summary of Triangle Techniques
- Operations with Vectors
- Vector Addition
- Vector Subtraction
- Resultant of Two Displacements
- Directed Line Segments
- Component Vectors
- Vector Multiplied by a Scalar
- Translation of Vectors and Slope
- Unit Vectors and Components
- Resultant as the Sum of Two Components
- Resultant as Magnitude and Direction

- Polar Coordinate System
- Plots of Polar Coordinates
- Distance Between Two Polar Coordinates
- Graphing Basic Polar Equations
- Transformations of Polar Graphs
- Graphing Polar Equations on the Calculator
- Polar to Rectangular Conversions
- Rectangular to Polar Conversions
- Rectangular to Polar Form for Equations
- Converting Equations Using Graphing Calculator
- Polar Curves
- Intersections of Polar Curves
- Equivalent Polar Curves
- Trigonometric Form of Complex Numbers
- Polar Form of a Complex Number
- Applications of Product and Quotient Theorems
- Product Theorem
- Quotient Theorem
- DeMoivre's Theorem and nth Roots
- DeMoivre's Theorem
- Equations Using DeMoivre's Theorem
- Geometry of Complex Roots

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