Other tags that relate to Trig Reps
Trigonometric identities. Maclaurin series. Trigonometric functions and graphs. Maths Supporting SET. Sine, cosine, tangent. Regular polygons and circles. Pythagoras' theorem. Complex numbers. Generalising. Investigations.There are 56 results
Broad Topics > Mathematical Thinking > Investigations
Sextet
Age 16 to 18 Challenge Level:
Investigate x to the power n plus 1 over x to the power n when x plus 1 over x equals 1.
A Rational Search
Age 16 to 18 Challenge Level:
Investigate constructible images which contain rational areas.
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.
Stirling Work
Age 16 to 18 Challenge Level:
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
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.
Two Regular Polygons
Age 14 to 16 Challenge Level:
Two polygons fit together so that the exterior angle at each end of their shared side is 81 degrees. If both shapes now have to be regular could the angle still be 81 degrees?
Bessel's Equation
Age 16 to 18 Challenge Level:
Get further into power series using the fascinating Bessel's equation.
Taking Trigonometry Series-ly
Age 16 to 18 Challenge Level:
Look at the advanced way of viewing sin and cos through their power series.
Building Approximations for Sin(x)
Age 16 to 18 Challenge Level:
Build up the concept of the Taylor series
What Do Functions Do for Tiny X?
Age 16 to 18 Challenge Level:
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Trig-trig
Age 16 to 18 Challenge Level:
Explore the properties of combinations of trig functions in this open investigation.
Chance of That
Age 16 to 18 Challenge Level:
What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?
Scale Invariance
Age 16 to 18 Challenge Level:
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Spirostars
Age 16 to 18 Challenge Level:
A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?
9 Hole Light Golf
Age 5 to 18 Challenge Level:
We think this 3x3 version of the game is often harder than the 5x5 version. Do you agree? If so, why do you think that might be?
Track Design
Age 14 to 16 Challenge Level:
Where should runners start the 200m race so that they have all run the same distance by the finish?
Genetic Intrigue
Age 16 to 18
Dip your toe into the fascinating topic of genetics. From Mendel's theories to some cutting edge experimental techniques, this article gives an insight into some of the processes underlying. . . .
Diamonds Aren't Forever
Age 16 to 18 Challenge Level:
Ever wondered what it would be like to vaporise a diamond? Find out inside...
The Power of Dimensional Analysis
Age 14 to 18
An introduction to a useful tool to check the validity of an equation.
Reaction Rates!
Age 16 to 18
Fancy learning a bit more about rates of reaction, but don't know where to look? Come inside and find out more...
Designing Table Mats
Age 11 to 16 Challenge Level:
Formulate and investigate a simple mathematical model for the design of a table mat.
Clear as Crystal
Age 16 to 18 Challenge Level:
Unearth the beautiful mathematics of symmetry whilst investigating the properties of crystal lattices
Big and Small Numbers in the Physical World
Age 14 to 16 Challenge Level:
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Smoke and Daggers
Age 16 to 18 Challenge Level:
We all know that smoking poses a long term health risk and has the potential to cause cancer. But what actually happens when you light up a cigarette, place it to your mouth, take a tidal breath. . . .
Big and Small Numbers in Chemistry
Age 14 to 16 Challenge Level:
Get some practice using big and small numbers in chemistry.
Inspect Your Gadgets
Age 16 to 18
Read about the mathematics behind the measuring devices used in quantitative chemistry
Perfect Eclipse
Age 14 to 16 Challenge Level:
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Alternative Record Book
Age 14 to 18 Challenge Level:
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Big and Small Numbers in the Living World
Age 11 to 16 Challenge Level:
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Robot Camera
Age 14 to 16 Challenge Level:
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Mach Attack
Age 16 to 18 Challenge Level:
Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.
There's Always One Isn't There
Age 14 to 16 Challenge Level:
Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.
Geometry and Gravity 1
Age 11 to 18
This article (the first of two) contains ideas for investigations. Space-time, the curvature of space and topology are introduced with some fascinating problems to explore.
Peeling the Apple or the Cone That Lost Its Head
Age 14 to 16 Challenge Level:
How much peel does an apple have?
Problem Solving: Opening up Problems
Age 5 to 16
All types of mathematical problems serve a useful purpose in mathematics teaching, but different types of problem will achieve different learning objectives. In generalmore open-ended problems have. . . .
A Different Differential Equation
Age 16 to 18 Challenge Level:
Explore the properties of this different sort of differential equation.
Few and Far Between?
Age 16 to 18 Challenge Level:
Can you find some Pythagorean Triples where the two smaller numbers differ by 1?
More Bridge Building
Age 16 to 18 Challenge Level:
Which parts of these framework bridges are in tension and which parts are in compression?
Making More Tracks
Age 16 to 18 Challenge Level:
Given the equation for the path followed by the back wheel of a bike, can you solve to find the equation followed by the front wheel?
Escape from Planet Earth
Age 16 to 18 Challenge Level:
How fast would you have to throw a ball upwards so that it would never land?
Powerfully Fast
Age 16 to 18 Challenge Level:
Explore the power of aeroplanes, spaceships and horses.
Snookered
Age 14 to 18 Challenge Level:
In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?
Operating Machines
Age 16 to 18 Challenge Level:
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
NRICH is part of the family of activities in the Millennium Mathematics Project.