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Exam-Style Question on Periodic GraphsA mathematics exam-style question with a worked solution that can be revealed gradually |
Question id: 712. This question is similar to one that appeared on an IB AA Higher paper in 2023. The use of a calculator is not allowed.
The function \(f\) is defined by \(f(x) = \cos{ax} \) , where \(a > 0\). The following diagram shows part of the graph of \(f\), where x is in radians. There are local maxima at \(x = b , 2b \text{ and } 3b\).
(a) Find an expression for \(b\) in terms of \(a\).
The function \(g\) is defined by \(g(x) = 2\cos{ \dfrac{bx}{3}} \)
(b) On the axes above, sketch the graph of \(g\).
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