Exact solutions of an equation in the cube of sine, then the same equation with a tripled angle
Exact solutions of an equation in the cube of sine, then the same equation with a tripled angle
IB Year 6 | Grade 12
6 marks
The function \(\mathrm{f}\) is given by \(\mathrm{f}(x)=2\sqrt2\sin^3x\).
- Find the exact solutions of the equation \(\mathrm{f}(x)=-1\) for \(-\pi\le x\le2\pi\).[4]
- Hence solve the equation \(\mathrm{f}(3x)=-1\) for \(-\dfrac{\pi}{3}\le x\le\dfrac{2\pi}{3}\).[2]
Solution:
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Answer:(a) \(x=-\dfrac{3\pi}{4},\ -\dfrac{\pi}{4},\ \dfrac{5\pi}{4},\ \dfrac{7\pi}{4}\) (b) \(x=-\dfrac{\pi}{4},\ -\dfrac{\pi}{12},\ \dfrac{5\pi}{12},\ \dfrac{7\pi}{12}\)
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