Trigonometry - Trigonometric Graphs and Parameters
Trigonometry - Trigonometric Graphs and Parameters
TGM Original Questions
The function \(f\) is defined, for \(0 \le x \le 2\pi\), by \(f(x) = -4\cos 2x + 1\).
- Sketch the graph of \(y = f(x)\) for \(0 \le x \le 2\pi\).
- By sketching a proper straight line on the same diagram, find the number of solutions to the equation \(2\pi \cos 2x - x + \pi = 0\) for \(0 \le x \le 2\pi\).
- Find the range of the value of \(k\) for which the equation \(-4\cos 2x + 1 - k = 0\) has more than two unique solutions for \(0 \le x \le 2\pi\).
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Answer:(i) See sketch. (ii) Draw \(y=3-\dfrac{2x}{\pi}\): 4 solutions. (iii) \(-3\le k<5\).
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