Sine, cosine, tangent

  • 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?
  • Figure of Eight
    problem
    Favourite

    Figure of Eight

    Age
    14 to 16
    Challenge level
    On a nine-point pegboard a band is stretched over 4 pegs in a "figure of 8" arrangement. How many different "figure of 8" arrangements can be made ?
  • Spokes
    problem
    Favourite

    Spokes

    Age
    16 to 18
    Challenge level
    Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.
  • Where is the dot?
    problem
    Favourite

    Where Is the Dot?

    Age
    14 to 16
    Challenge level

    A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?

  • Sine and Cosine
    problem
    Favourite

    Sine and Cosine

    Age
    14 to 16
    Challenge level

    The sine of an angle is equal to the cosine of its complement. Can you explain why and does this rule extend beyond angles of 90 degrees?

  • Five green equilateral triangles, arranged to almost make a complete pentagon.
    problem
    Favourite

    Doesn't Add Up

    Age
    14 to 16
    Challenge level

    In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

  • Inscribed in a Circle
    problem
    Favourite

    Inscribed in a Circle

    Age
    14 to 16
    Challenge level

    The area of a square inscribed in a circle with a unit radius is 2. What is the area of these other regular polygons inscribed in a circle with a unit radius?

  • Cosines Rule
    problem
    Favourite

    Cosines Rule

    Age
    14 to 16
    Challenge level

    Three points A, B and C lie in this order on a line, and P is any point in the plane. Use the Cosine Rule to prove the following statement.

  • Far Horizon
    problem
    Favourite

    Far Horizon

    Age
    14 to 16
    Challenge level

    An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

  • 8 Methods for Three By One
    problem
    Favourite

    8 Methods for Three by One

    Age
    14 to 18
    Challenge level

    This problem in geometry has been solved in no less than EIGHT ways by a pair of students. How would you solve it? How many of their solutions can you follow? How are they the same or different? Which do you like best?

Displaying 1 - 10 of 56