Trigonometry

  1. Trigonometric Functions of Any Angle
    1. The Unit Circle
      1. Definition and Properties
        1. Circle with Radius 1
          1. Center at Origin
            1. Equation x² + y² = 1
            2. Coordinates on the Unit Circle
              1. Relationship to Trigonometric Functions
                1. x-coordinate as Cosine
                  1. y-coordinate as Sine
                  2. Key Points on Unit Circle
                    1. Quadrantal Points
                      1. Special Angle Points
                        1. Memorization Strategies
                      2. Symmetry in the Unit Circle
                        1. x-axis Symmetry
                          1. y-axis Symmetry
                            1. Origin Symmetry
                              1. Applications of Symmetry
                            2. Extending Trigonometric Functions Beyond Acute Angles
                              1. Definitions Based on Coordinates
                                1. Point (x, y) on Terminal Side
                                  1. Distance r from Origin
                                    1. Sine as y/r
                                      1. Cosine as x/r
                                        1. Tangent as y/x (x ≠ 0)
                                          1. Reciprocal Function Definitions
                                            1. Cosecant as r/y (y ≠ 0)
                                              1. Secant as r/x (x ≠ 0)
                                                1. Cotangent as x/y (y ≠ 0)
                                              2. Signs of Trigonometric Functions by Quadrant
                                                1. Quadrant I
                                                  1. All Functions Positive
                                                  2. Quadrant II
                                                    1. Sine Positive, Others Negative
                                                    2. Quadrant III
                                                      1. Tangent and Cotangent Positive
                                                      2. Quadrant IV
                                                        1. Cosine and Secant Positive
                                                      3. ASTC Memory Device
                                                        1. All Students Take Calculus
                                                          1. Application to Sign Determination
                                                        2. Reference Angles
                                                          1. Definition of Reference Angle
                                                            1. Acute Angle to x-axis
                                                              1. Always Between 0° and 90°
                                                              2. Finding Reference Angles
                                                                1. Quadrant I: Angle Itself
                                                                  1. Quadrant II: 180° - Angle
                                                                    1. Quadrant III: Angle - 180°
                                                                      1. Quadrant IV: 360° - Angle
                                                                      2. Evaluating Functions Using Reference Angles
                                                                        1. Function Value Magnitude
                                                                          1. Sign from Quadrant
                                                                            1. Complete Evaluation Process
                                                                          2. Trigonometric Values for Quadrantal Angles
                                                                            1. Values at 0° (0 radians)
                                                                              1. Values at 90° (π/2 radians)
                                                                                1. Values at 180° (π radians)
                                                                                  1. Values at 270° (3π/2 radians)
                                                                                    1. Values at 360° (2π radians)
                                                                                      1. Undefined Values
                                                                                        1. When and Why Functions are Undefined
                                                                                          1. Geometric Interpretation

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                                                                                      2. Right Triangle Trigonometry

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                                                                                      4. Graphs of Trigonometric Functions