# Exam-Style Question on Periodic Functions

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 391. This question is similar to one that appeared on an IB AA Standard paper (specimen) for 2021. The use of a calculator is allowed.

Consider a function $$f$$, such that $$f(x)=7.2\sin(\frac{\pi}{6}x + 2) + b$$ where $$0\le x \le 12$$

(a) Find the period of $$f$$.

The function $$f$$ has a local maximum at the point (11.18,10.3) , and a local minimum at (5.18.-4.1).

(b) Find the value of b.

(c) Hence, find the value of $$f(7)$$.

A second function $$g$$ is given by $$g(x)=a\sin(\frac{2\pi}{7}(x -4)) + c$$ where $$0 \le x \le 10$$

The function $$g$$ passes through the points (2.25,-3) and (5.75,7).

(d) Find the value of $$a$$ and the value of $$c$$.

(e) Find the value of x for which the functions have the greatest difference.

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