Trigonometry - Trigonometric Graphs and Parameters
Trigonometry - Trigonometric Graphs and Parameters
TGM Original Questions
The diagram shows part of the graph of \(y = a \cos bx\), where \(b > 0\), for \(0 \le x \le \frac{4\pi}{3}\).
- Find the amplitude, the period and the range of values of \(y\) corresponding to the interval. Hence find the values of \(a\) and \(b\).
- Write down the coordinates of the maximum point(s) and the minimum point(s) of the graph in the given interval.
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Answer:(i) amplitude \(8\), period \(\dfrac{2\pi}{3}\), range \(-8 \le y \le 8, a = 8, b = 3\); (ii) maxima \((0,8), \left(\dfrac{2\pi}{3},8\right), \left(\dfrac{4\pi}{3},8\right)\); minima \(\left(\dfrac{\pi}{3},-8\right), (\pi ,-8)\)
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