Geometry & Trigonometry

In this topic, we will look at

  • Trigonometric Functions
  • The Unit Circle
  • Trigonometric Identities
  • Solving Trigonometric Equations
  • Triangle Geometry
  • Vectors and Angles
  • Equation of Lines
  • Kinematics
  • Intersections
  • Vector Product
  • Equation of Planes


  • Triangle Geometry

    In this page, we will look at the Sine Rule, the Cosine Rule and the formula for the Area of a Triangle. The formula for these three are fairly straight forward to use, but don't take this topic too lightly, sometimes the exam questions can be quite challe

  • Unit CircleSL

    The Unit Circle is probably the most important topic to understand from the whole of trigonometry. Lots of the properties of the trigonometric functions can be found from the unit circle. All the work on this page will help us understand all of these prope

  • Unit Circle HL

    The Unit Circle is probably the most important topic to understand from the whole of trigonometry. Lots of the properties of the trigonometric functions can be found from the unit circle. All the work on this page will help us understand all...

  • Trigonometric Identities

    In this page, we will will learn about the Pythagorean Identities and the Double Angle Formulae used in Trigonometry. It is actually quite rare that exam questions are solely about these identities, but it is essential that you can use and manipulate them

  • Solving Trigonometric Equations

    Solving trigonometric equations is a common topic on the examination. The key to solving them is a good knowledge of the trigonometric functions. Whether you prefer to use the Unit Circle or the graphs of the functions, you need to a method that works for

  • Vectors and Angles

    In this topic, we will look at finding the angle between vectors in different circumstances. The whole topic revolves around the scalar (or dot) product. Often we are concerned with perpendicular vectors, and the fact that the scalar product equals zero in

  • Equation of a Line

    You should already be familiar with the equation of a straight line in Cartesian form in 2 dimensions, y = ax + b. When we move into 3 dimensions, the Cartesian form becomes a little more awkward. Don't worry, vectors are here to help us out! Once you unde

  • Intersection of Lines

    This page looks at the intersections of lines in 2 and 3 dimensions. In 2D, lines intersect or are parallel. In 3D, it is slightly more complicated, they can intersect or be parallel or be skew (not parallel and not intersect!). We will also look at applic

  • Kinematics

      This page is all about kinematics for vectors. You can describe the position of a moving object using vectors. This is very much like the equation of a straight line except that the parameter is t for time. The equation below is an example:...

  • Vector Product

      These are sequences where you go from term to term by adding a common difference. The sequence in the image 1, 5 , 9 has a common difference of 4 since we add 4 to the previous term. There are formula in the booklet to help you with this...

  • Equations of Planes

    This is a hugely important topic in the HL course. We can describe planes in 3D in a number of different ways. It is not enough to learn the different equations, but it is vital that you have a strong conceptual understanding of the different forms of the

  • Intersection of Planes

    This page is all about how planes meet (or not). Two planes will either be parallel or meet at a line. Three planes will either 1) not meet - zero solutions, 2) meet at a point - unique solution, or 3) meet at a line (or plane) - infinite solutions. We wil

  • Intersection of Line and Plane

    For questions involving lines and planes, we are usually asked to find the point of intersection. However, when we consider a line and a plane, there are three possible situations. In this page, we will consider all the possible outcomes. 1) the line in