Trigonometry and Plane Geometry

• Why sin(30˚) equals 1/2
• Sin, Cos, Tan and the Unit Circle
• Application of Trigonometry and Pythagoras' Theorem
• Application of the Cosine Rule (Law Of Cosines)
• Problem solving with Trigonometry and Linear Equations
• Problem Solving using Pythagoras' Theorem
• The Perpendicular Distance from a Point to a Line
• Plane Geometry Problem Part 1 - Line tangent to Unit Circle
• Plane Geometry Problem Part 2 - Area of Trapezium Enclosing a Circle
• Plane Geometry Problem Part 3 - Minimum Area of a Trapezium
• Locus in the Cartesian Plane - Part 1
• Locus in the Cartesian Plane - Part 2

Conic Sections

• Introduction to Conic Sections
• Conic Sections - Focus, Directrix and Eccentricity
• Conic Sections: The Parabola, e = 1
• Conical Form of Parabolas - What is the Focus and Directrix?
• Conics - Focus and Directrix for Horizontal Parabolas
• Conic Sections: The Ellipse - Part 1
• Conic Sections: The Ellipse - Part 2
• Ellipses - Example 1: Sketching 4x² + 9y² = 36
• Ellipses - Example 2: Finding the Equation
• Equation for ellipses not centred at Origin
• Equation for ellipse with vertical Major Axis
• Conic Sections: The Hyperbola - Part 1
• Conic Sections: The Hyperbola - Part 2
• Hyperbolas - Example 1: Sketching x²/16 - y²/48 = 1
• North-South opening Hyperbolas
• Equation for Hyperbolas translated from Origin
• Polar Form of Conic Sections - Part 1
• Polar Form of Conic Sections - Part 2
• Polar Conics Example 1 - Sketch r=3/(2+2cos
  θ
  )
• Polar Conics Example 2 - Sketch r=12/(6+2sinθ)

Trigonometric Identities

• Proof of the Sum-Difference Formulas - Part 1
• Proof of the Sum-Difference Formulas - Part 2
• Deriving the Product to Sum Formulas
• Expressing sin(x) and cos(x) in terms of tan(x)
• Expressing sin(x) and cos(x) in terms of t = tan(x/2)