Trigonometric identities

  • Three by One
    problem
    Favourite

    Three by One

    Age
    16 to 18
    Challenge level

    There are many different methods to solve this geometrical problem - how many can you find?

  • Octa-flower
    problem
    Favourite

    Octa-Flower

    Age
    16 to 18
    Challenge level

    Join some regular octahedra, face touching face and one vertex of each meeting at a point. How many octahedra can you fit around this point?

  • t for Tan
    problem
    Favourite

    T for Tan

    Age
    16 to 18
    Challenge level

    Can you find a way to prove the trig identities using a diagram?

  • Shape and territory
    problem
    Favourite

    Shape and Territory

    Age
    16 to 18
    Challenge level

    If for any triangle ABC tan(A - B) + tan(B - C) + tan(C - A) = 0 what can you say about the triangle?

  • Loch Ness
    problem
    Favourite

    Loch Ness

    Age
    16 to 18
    Challenge level

    Draw graphs of the sine and modulus functions and explain the humps.

  • Sine and Cosine for Connected Angles
    problem

    Sine and Cosine for Connected Angles

    Age
    14 to 16
    Challenge level
    The length AM can be calculated using trigonometry in two different ways. Create this pair of equivalent calculations for different peg boards, notice a general result, and account for it.
  • Reflect Again
    problem

    Reflect Again

    Age
    16 to 18
    Challenge level
    Follow hints to investigate the matrix which gives a reflection of the plane in the line y=tanx. Show that the combination of two reflections in intersecting lines is a rotation.
  • Quaternions and Rotations
    problem

    Quaternions and Rotations

    Age
    16 to 18
    Challenge level
    Find out how the quaternion function G(v) = qvq^-1 gives a simple algebraic method for working with rotations in 3-space.
  • Quaternions and Reflections
    problem

    Quaternions and Reflections

    Age
    16 to 18
    Challenge level
    See how 4 dimensional quaternions involve vectors in 3-space and how the quaternion function F(v) = nvn gives a simple algebraic method of working with reflections in planes in 3-space.
  • Trig reps
    problem

    Trig Reps

    Age
    16 to 18
    Challenge level

    Can you deduce the familiar properties of the sine and cosine functions starting from these three different mathematical representations?

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