## Exam-Style Questions on Periodic Functions## Problems on Periodic Functions adapted from questions set in previous Mathematics exams. |

## 1. | IB Analysis and Approaches |

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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