Sine, cosine, tangent

problem
Stadium sightline

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?
problem
Degree ceremony

Age

16 to 18

Challenge level

Can you find the sum of the squared sine values?
problem
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.
problem
Three by one

Age

16 to 18

Challenge level

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

Age

16 to 18

Challenge level

Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?