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Salut!

You can find the parameter b by finding the period of the function:

and using this formula:

The period of a function is the interval in x that it takes to complete a cycle. In your exercise, you have a complete cycle here:

So the period is:
$$p=\frac{10 \pi}{3}-\frac{ 2\pi}{3}=\frac{8\pi}{3}$$

Using the previous formula, we can then find the absolute value of the parameter b:
$$p=\frac{2\pi}{|b|}$$
$$\frac{8\pi}{3}=\frac{2\pi}{|b|}$$
$$|b|=2\pi \times \frac{3}{8\pi}$$
$$|b|=\frac{2\times 3}{8}$$
$$|b|=\frac{6}{8}=\frac{3}{4}$$

Since the sign of b does not change the shape of the curve, the simplest thing is to choose the positive value.
$$b=\frac{3}{4}$$

There you go! :D Here's a sheet on this concept that presents similar examples: Finding the Rule of a Cosine Function | Secondaire | Alloprof

Let us know if we can help you with anything else! :)