Cosine modeling of a spot of paint on the wheel of a paddle-steamer

Question

A paint spot $X$ lies on the outer rim of the wheel of a paddle-steamer. The wheel has radius $3$m and as it rotates at a constant rate, ${X}$ is seen entering the water every $4$ seconds. $H$ is the distance of $X$ above the bottom of the boat. At time $t=0$, $X$ is at its highest point. Find the cosine model $H(t)=A \cos B(t-C)+D$

My try: Since the point $X$ reaches water every $4$ seconds, we have $B=\frac{\pi}{2}$

Now since the lowest point is diametrically opposite to the highest point of $X$ we have the amplitude as $A=\frac{7-1}{2}=3$. Thus we have $$H(t)=3\cos\left(\frac{\pi}{2}(t-C)\right)+D$$ Since at $t=0$ we have $H=7$, using the cosine model we get $$3\cos\left(-\frac{\pi}{2}C\right)+D=7 \to (1)$$ But how to find $C,D$?

Answer 1

Hint:

$3\cos X+D=7 \implies D = 4, X = 0$ (or a multiple of $2\pi$).