Calculating k degrees

[wicked inlet]

Hey all. Stuck on question c here. My working out for the rest of the question is as written.

[wicked inlet]

I did a reverse calculation using the answer in the workbook k=32 and got the right height at 25m.
I'm struggling to figure how to calculate k in the cos bracket:

[slow parcel]

You're probably confused because the inverse cosine of 1 is and therefore k should be equal to 0. This is actually a valid solution, but in the context of the problem it would mean that the water level is constant.

Remember that the cosine has a local maximum at every multiple of $2\pi$, so the equation can be rewritten as

$\newline 1=\cos\left(11.25k-2\pi n\right)\newline$

Now you just need to solve for $n = 1$ and convert to degrees.

[glossy jewel]

solarunes