Sine, cosine, tangent

  • So Big
    problem
    Favourite

    So Big

    Age
    16 to 18
    Challenge level

    One side of a triangle is divided into segments of length a and b by the inscribed circle, with radius r. Prove that the area is: abr(a+b)/ab-r^2

  • 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.

  • Coke machine
    problem

    Coke Machine

    Age
    14 to 16
    Challenge level
    The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...
  • 30-60-90 Polypuzzle
    problem

    30-60-90 Polypuzzle

    Age
    16 to 18
    Challenge level
    Re-arrange the pieces of the puzzle to form a rectangle and then to form an equilateral triangle. Calculate the angles and lengths.
  • Sine Problem
    problem

    Sine Problem

    Age
    16 to 18
    Challenge level
    In this 'mesh' of sine graphs, one of the graphs is the graph of the sine function. Find the equations of the other graphs to reproduce the pattern.
  • Farhan's Poor Square
    problem

    Farhan's Poor Square

    Age
    14 to 16
    Challenge level
    From the measurements and the clue given find the area of the square that is not covered by the triangle and the circle.
  • Small Steps
    problem

    Small Steps

    Age
    16 to 18
    Challenge level
    Two problems about infinite processes where smaller and smaller steps are taken and you have to discover what happens in the limit.
  • Bend
    problem

    Bend

    Age
    16 to 18
    Challenge level
    What is the longest stick that can be carried horizontally along a narrow corridor and around a right-angled bend?
  • Diagonals for Area
    problem

    Diagonals for Area

    Age
    16 to 18
    Challenge level
    Can you prove this formula for finding the area of a quadrilateral from its diagonals?
  • Screen Shot
    problem

    Screen Shot

    Age
    14 to 16
    Challenge level
    A moveable screen slides along a mirrored corridor towards a centrally placed light source. A ray of light from that source is directed towards a wall of the corridor, which it strikes at 45 degrees before being reflected across to the opposite wall and so on until it hits the screen.
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