Range of a scaled sine used to solve an equation with a cosine of a sine
Range of a scaled sine used to solve an equation with a cosine of a sine
IB Year 6 | Grade 12
7 marks
- Write down the minimum value and the maximum value of \(\frac{\pi}{2}\sin x\).[1]
- Hence solve the equation \(4\cos^2\left(\frac{\pi}{2}\sin x\right)=2\) for \(0\le x\le2\pi\).[6]
Solution:
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Answer:(a) Minimum \(-\frac{\pi}{2}\), maximum \(\frac{\pi}{2}\) (b) \(x=\frac{\pi}{6},\ \frac{5\pi}{6},\ \frac{7\pi}{6},\ \frac{11\pi}{6}\)
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