Trigonometry - Trigonometric Graphs and Parameters
Trigonometry - Trigonometric Graphs and Parameters
TGM Original Questions
The diagram shows the graphs of \(y = -2 \sin kx\) and \(y = -\cos mx - 3\) for \(0 \leq x \leq \pi\). The curves have a common turning point \(Q\) (maximum or minimum point). Find
- the values of \(k\) and \(m\),
- the coordinates of \(Q\), and
- the coordinates of the next common turning point of the two curves (in the positive \(x\)-direction).
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Answer:(i) \(k = 3, m = \dfrac{6}{5}\); (ii) \(Q = \left(\dfrac{5\pi}{6}, -2\right)\); (iii) \(\left(\dfrac{25\pi}{6}, -2\right)\)
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