Question

A roof in the shape of an upside down cosine wave is to be built to cover an arena. The arena is 24 m wide, the height of the roof at either side wall is 5 m, and the max height of the roof is 9m .
write the function that gives the height of the roof in terms of the distance from the left wall.
What is the height of the roof 10m from the left wall.

Answer 1

since we have a max height of f(12)=9, we have a simple shifted cosine wave, of the form

y = 9 cos(k(x-12))

That will give us an amplitude of height 9, such that f(12) = 9. Now we need to figure what k is.

we know that f(0) = 5
5 = 9cos(-12k) = 9 cos(12k)

k = 1/12 * cos^-1(5/9) = 0.0818

So, f(x) = 9cos(0.0818(x-12))

f(10) = 8.88

as it should be, since 10 is close to 12, f(10) is close to f(12) = 9.