Number of solutions of a cosine equation with a parameter
Number of solutions of a cosine equation with a parameter
IP 3
8 marks
- Sketch the graph of \(y=3\cos 2x+1\) for \(0\le x\le\pi\), showing the coordinates of its maximum and minimum points.[3]
- Find the set of values of the constant \(k\) for which the equation \(3\cos 2x+1=k\) has exactly two solutions in \(0\le x\le\pi\). Justify your answer, including the end values.[3]
- Solve \(3\cos 2x+1=2.5\) for \(0\le x\le\pi\), giving exact answers.[2]
Solution:
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Answer:(a) maximum \((0,4)\) and \((\pi,4)\), minimum \(\left(\dfrac{\pi}{2},-2\right)\) (b) \(-2<k\le 4\) (c) \(x=\dfrac{\pi}{6},\ \dfrac{5\pi}{6}\)
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