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  #### Resources tagged with Sine, cosine, tangent similar to Weird Universes:
  
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  ### There are 59 results
  
  Broad Topics > Pythagoras and Trigonometry > Sine, cosine, tangent
  
  ### Over the Pole
  
  ##### Age 16 to 18 Challenge Level:
  
  Two places are diametrically opposite each other on the same line of latitude. Compare the distances between them travelling along the line of latitude and travelling over the nearest pole.
  
  ### Flight Path
  
  ##### Age 16 to 18 Challenge Level:
  
  Use simple trigonometry to calculate the distance along the flight path from London to Sydney.
  
  ### 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.
  
  ### 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.
  
  ### Belt
  
  ##### Age 16 to 18 Challenge Level:
  
  A belt of thin wire, length L, binds together two cylindrical welding rods, whose radii are R and r, by passing all the way around them both. Find L in terms of R and r.
  
  ### Pythagoras on a Sphere
  
  ##### Age 16 to 18 Challenge Level:
  
  Prove Pythagoras' Theorem for right-angled spherical triangles.
  
  ### 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.
  
  ### Eight Ratios
  
  ##### Age 14 to 16 Challenge Level:
  
  Two perpendicular lines lie across each other and the end points are joined to form a quadrilateral. Eight ratios are defined, three are given but five need to be found.
  
  ##### Age 14 to 18 Challenge Level:
  
  How would you design the tiering of seats in a stadium so that all spectators have a good view?
  
  ### Diagonals for Area
  
  ##### Age 16 to 18 Challenge Level:
  
  Can you prove this formula for finding the area of a quadrilateral from its diagonals?
  
  ### The History of Trigonometry- Part 1
  
  ##### Age 11 to 18
  
  The first of three articles on the History of Trigonometry. This takes us from the Egyptians to early work on trigonometry in China.
  
  ### Moving Squares
  
  ##### Age 14 to 16 Challenge Level:
  
  How can you represent the curvature of a cylinder on a flat piece of paper?
  
  ### Geometric Trig
  
  ##### Age 16 to 18 Short Challenge Level:
  
  Trigonometry, circles and triangles combine in this short challenge.
  
  ### History of Trigonometry - Part 3
  
  ##### Age 11 to 18
  
  The third of three articles on the History of Trigonometry.
  
  ### Pumping the Power
  
  ##### Age 16 to 18 Challenge Level:
  
  What is an AC voltage? How much power does an AC power source supply?
  
  ### 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?
  
  ### 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?
  
  ### 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?
  
  ### 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?
  
  ### Trigonometric Protractor
  
  ##### Age 14 to 16 Challenge Level:
  
  An environment that simulates a protractor carrying a right- angled triangle of unit hypotenuse.
  
  ### Raising the Roof
  
  ##### Age 14 to 16 Challenge Level:
  
  How far should the roof overhang to shade windows from the mid-day sun?
  
  ### A Scale for the Solar System
  
  ##### Age 14 to 16 Challenge Level:
  
  The Earth is further from the Sun than Venus, but how much further? Twice as far? Ten times?
  
  ### Ball Bearings
  
  ##### Age 16 to 18 Challenge Level:
  
  If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.
  
  ##### Age 14 to 16 Challenge Level:
  
  The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.
  
  ### Degree Ceremony
  
  ##### Age 16 to 18 Challenge Level:
  
  What does Pythagoras' Theorem tell you about these angles: 90°, (45+x)° and (45-x)° in a triangle?
  
  ### 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?. . . .
  
  ##### Age 14 to 16 Challenge Level:
  
  If you were to set the X weight to 2 what do you think the angle might be?
  
  ### Dodecawhat
  
  ##### Age 14 to 16 Challenge Level:
  
  Follow instructions to fold sheets of A4 paper into pentagons and assemble them to form a dodecahedron. Calculate the error in the angle of the not perfectly regular pentagons you make.
  
  ### 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?
  
  ### Round and Round a Circle
  
  ##### Age 14 to 16 Challenge Level:
  
  Can you explain what is happening and account for the values being displayed?
  
  ### History of Trigonometry - Part 2
  
  ##### Age 11 to 18
  
  The second of three articles on the History of Trigonometry.
  
  ### Logosquares
  
  ##### Age 16 to 18 Challenge Level:
  
  Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.
  
  ### 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?
  
  ### At a Glance
  
  ##### Age 14 to 16 Challenge Level:
  
  The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
  
  ### Circle Scaling
  
  ##### Age 14 to 16 Challenge Level:
  
  Describe how to construct three circles which have areas in the ratio 1:2:3.
  
  ### Inscribed in a Circle
  
  ##### Age 14 to 16 Challenge Level:
  
  The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?
  
  ##### Age 11 to 18
  
  Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.
  
  ### 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?
  
  ### 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. . . .
  
  ### Orbiting Billiard Balls
  
  ##### Age 14 to 16 Challenge Level:
  
  What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?
  
  ### 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 ?
  
  ### 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.
  
  ### Squ-areas
  
  ##### Age 14 to 16 Challenge Level:
  
  Three squares are drawn on the sides of a triangle ABC. Their areas are respectively 18 000, 20 000 and 26 000 square centimetres. If the outer vertices of the squares are joined, three more. . . .
  
  ### Circle Box
  
  ##### Age 14 to 16 Challenge Level:
  
  It is obvious that we can fit four circles of diameter 1 unit in a square of side 2 without overlapping. What is the smallest square into which we can fit 3 circles of diameter 1 unit?
  
  ### Round and Round
  
  ##### Age 14 to 16 Challenge Level:
  
  Prove that the shaded area of the semicircle is equal to the area of the inner circle.
  
  ### 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.
  
  ##### 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?
  
  ### 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...
  
  ### Six Discs
  
  ##### Age 14 to 16 Challenge Level:
  
  Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?
  
  ### From All Corners
  
  ##### Age 14 to 16 Challenge Level:
  
  Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.