The equation of a wave is given as ay = b sin cx where a, b and c are integers. Given that the amplitude of the wave is 1 2/3 and the period is 90°, find the sum of a, b and c.

The given equation is $ay = b \sin cx$.
Divide by $a$ (assuming $a \neq 0$):

$$y = \frac{b}{a} \sin cx$$

In this standard form, the amplitude is $|A|$ and the period is $\frac{360^\circ}{|B|}$ when the angle is in degrees. Here, $A = \frac{b}{a}$ and $B = c$.

The amplitude is given as $1\frac{2}{3}$. Convert this to an improper fraction:

$$1\frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{5}{3}$$

So, the amplitude is $\left|\frac{b}{a}\right| = \frac{5}{3}$.
Since $a$ and $b$ are integers, and typically we look for the simplest positive integer values unless specified otherwise, we can set $\frac{b}{a} = \frac{5}{3}$.
This implies $a=3$ and $b=5$.

The period is given as $90^\circ$.
Using the formula for the period:

$$\frac{360^\circ}{|c|} = 90^\circ$$

Solve for $|c|$:

$$|c| = \frac{360^\circ}{90^\circ} = 4$$

Since $c$ is an integer, $c$ can be 4 or $-4$. Assuming the simplest positive integer value for $c$, we take $c=4$.

Using the values $a=3$, $b=5$, and $c=4$:

$$a+b+c = 3+5+4 = 12$$

The sum of $a, b,$ and $c$ is $\boxed{12}$.

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