Trigonometry

Breadcrumb Abstract Shape
Breadcrumb Abstract Shape

1-Angle Measure and Special Triangles

  • Definition of Trigonometry.
  • Definition of an Angle.
  • Complementary and Supplementary Angles.
  • Decimal Degree and DMS of Angles.
  • Standard Position of an Angle.
  • Co-terminal Angles.
  • Pythagorean Theorem.
  • Special Angles.

2-Propertities of Triangles and Similar Triangles.

  • Classification of Triangles by Angles and by Sides.
  • Properties of Triangles.
  • Similar Triangles.

3-View from Trigonometry Coordinate Plane.

  • The Six Trigonometry Functions

o The Three Basic Trigonometry Functions.

o The Three Reciprocal Trigonometry Functions.

  • Trigonometry Quadrants.
  • Quadrantal Angles.

4-Fundamental Identities and Families of Identities.

  • Definition of Identities.
  • Reciprocal Identities.
  • Quotient (Ratio) Identities.
  • Pythagorean Identities
  • Verification of Identities.

5-A Right Triangle View of Trigonometry

  • Finding the Sides and Angles of Right Triangle.
  • Co-function Identities (Complementary Angle Identities).

6-Solving Right Triangles

  • Finding the Angles of Right Triangles Using Inverses.
  • Finding the Angles and Sides of a right Triangle.

7-Applications of Right Triangles

  • Angle of Elevation and Angle of Depression.
  • Special Pairs of Angles.
  • Applications of Right Triangles.

8-Extending Beyond Acute Angles

  • Definition of Reference Angles.
  • Reference Angles.
  • Table of Special Reference Angles.

9-Angle Measure in Radians

  • Central Angle and Central Circle.
  • Definition of Radian Angle.
  • Arc Length.
  • Changing from Degrees to Radians.
  • Changing from Radians to Degrees.
  • Co-terminal Angles in radians.

10-Angular Velocity, Linear Velocity and Area of a Circular Sector

  • Arc Length.
  • Angular Velocity
  • Linear (Tangential) Velocity.
  • Applications of Angular / Linear (Tangential) Velocity.

11-Unit Circle

  • Definition of Unit Circle.
  • Values (Ordered Pairs) of Trigonometric Functions with Unit Circle.
  • Finding (Ordered Pairs) of Trigonometric Functions with Unit Circle.

12-The Trigonometry of Real Numbers

  • The Reference Arc.

13-Graphs of Sine and Cosine Functions

  • Graph of Sine Function.
  • Graph of Cosine Function.

14-Transformations of Trigonometric Graphs

  • Transformations of Trigonometric Graphs.

15-Trigonometric Identities

  • Trigonometric Identities.

16-Sum and Difference Identities

  • Sum and Difference Identities.

17-Double-Angle, Half-Angle and Power Reducing Identities

  • Double-Angle Identity.
  • Half-Angle Identity.
  • Power Reducing Identity.

18-Product-to-Sum and Sum-to-Product Identities

  • Product-to-Sum Identity.
  • Sum-to-Product Identity.

19-The Inverse Trigonometric Functions

  • Sine Inverse Function.
  • Cosine Inverse Function.
  • Tangent Inverse Function.
  • Cosecant Inverse Function.
  • Secant Inverse Function.
  • Cotangent Inverse Function.

20- Solving Basic Trigonometric Equations

  • Solving Basic Trigonometric Equations.

21- Solving Advanced Trigonometric Equations

  • Solving Advanced Trigonometric Equations.

22- Oblique Triangles

  • Law of Sines.
  • Law of Cosines.

23- Area of a Triangle

  • Formulas used to find the Area of Triangles.
  • Bearing.
  • Heading.

24- Vectors and Vector Diagrams

  • Difference of Vector and Scalar.
  • Standard Vector Position.
  • Vector Components
  • Vector addition, Subtraction and Multiplication.
  • Vector Resultant.
  • Unit Vector.
  • Horizontal and Vertical Unit Vectors.
  • Linear Combination Form and Component Form of a Vector.

25- Vector Applications and Dot Product

  • Vector Equilibrium.
  • Dot Product (Scalar Product) of Vectors.
  • Angle between two Vectors.
  • Vector Component along on another Vector
  • Vector Projection along on another Vector
  • Inclination Angle.

26- Complex Numbers in Trigonometric Form

  • Complex Plane.
  • Rectangular Form of Complex Numbers.
  • Trigonometric Form of Complex Numbers.
  • Multiplying and Dividing Trigonometric Form.
  • Multiplying and Dividing Rectangular Form

27- De Moivre’s Theorem and the Theorem of Roots

  • De Moivre’s Theorem ( Power of Complex Numbers )
  • N-th Roots Theorem

28- Polar Coordinates, Equations and Graphs

  • Difference between Polar Coordinates and Rectangular Coordinates.
  • Converting from Polar Coordinates to Rectangular Coordinates.
  • Converting from Rectangular Coordinates to Polar Coordinates.
  • Symmetry of Polar Coordinates.
  • Graphing of Polar Coordinates (Polar Curves).
  • Changing Rectangular Equations to Polar Equations.
  • Changing Polar Equations to Rectangular Equations.

29- Parametric Equations and Graphs

  • Definition of Parametric Equations.
  • Graphing of Parametric Equations.