Precalculus

  1. Applications of Trigonometry
    1. Law of Sines
      1. Statement of the Law
        1. Solving Triangles with Law of Sines
          1. AAS Case
            1. ASA Case
              1. SSA Case (Ambiguous Case)
              2. The Ambiguous Case
                1. No Triangle
                  1. One Triangle
                    1. Two Triangles
                  2. Law of Cosines
                    1. Statement of the Law
                      1. Solving Triangles with Law of Cosines
                        1. SAS Case
                          1. SSS Case
                          2. Applications to Real-World Problems
                            1. Relationship to Pythagorean Theorem
                            2. Area of Triangles
                              1. Area Using Base and Height
                                1. Area Using Two Sides and Included Angle
                                  1. Heron's Formula
                                    1. Semi-perimeter
                                      1. Application of Heron's Formula
                                      2. Area Using Two Angles and One Side
                                      3. Vectors
                                        1. Introduction to Vectors
                                          1. Scalar vs Vector Quantities
                                            1. Geometric Representation
                                            2. Component Form of Vectors
                                              1. Horizontal and Vertical Components
                                                1. Position Vectors
                                                2. Vector Operations
                                                  1. Vector Addition
                                                    1. Parallelogram Method
                                                      1. Component Method
                                                      2. Vector Subtraction
                                                        1. Scalar Multiplication
                                                        2. Unit Vectors
                                                          1. Definition and Properties
                                                            1. Standard Unit Vectors i and j
                                                              1. Finding Unit Vectors
                                                              2. Direction Angles and Direction Cosines
                                                                1. Applications of Vectors
                                                                  1. Force Problems
                                                                    1. Velocity Problems
                                                                      1. Displacement Problems
                                                                    2. Dot Product
                                                                      1. Definition of Dot Product
                                                                        1. Component Formula
                                                                          1. Geometric Formula
                                                                          2. Properties of Dot Product
                                                                            1. Angle Between Two Vectors
                                                                              1. Orthogonal Vectors
                                                                                1. Vector Projections
                                                                                  1. Work as a Dot Product

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                                                                                6. Analytic Trigonometry

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                                                                                8. Polar Coordinates and Complex Numbers