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Question 53

The first inequality yields $0\leq x\leq\frac{\pi}{4}$ or $\frac{3\pi}{4}\leq x \leq\pi$ and the second inequality achieves equality when $2x=\frac{\pi}{6}$ or $\frac{5\pi}{6}$ therefore $x=\frac{\pi}{12}$ or $\frac{5\pi}{12}$. This inequality is satisfied for $\frac{\pi}{12} \leq x \leq \frac{5\pi}{12}$.
Both inequalities are satisfied for $\frac{\pi}{12} \leq x \leq \frac{\pi}{4}$ and $\frac{\pi}{4}-\frac{\pi}{12}=\frac{\pi}{6}$.
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  • Home
  • Tutor profile
  • Solutions
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  • Contact
  • Time saving
  • Speed hints
  • Testimonials/Statistics
  • Specimen solutions
  • 2016 Solutions
  • 2017 Solutions
  • 2018 Solutions
  • 2019 Solutions
  • 2020 Solutions
  • 2021 Solutions
  • New Specimen Solutions
  • NSAA Specimen Section 2 solutions
  • NSAA 2016 Section 2 Solutions
  • NSAA 2017 Section 2 Solutions
  • NSAA Tuition and eBook
  • PAT Tuition
  • Physics Aptitude Test Mock Papers
  • MAT Tuition
  • STEP Tuition
  • Maths Challenge and BMO Tuition
  • Advance Preparation Programme
  • Physics Degree Tuition
  • Maths enrichment tuition
  • Maths for Economics Degrees Tuition
  • GDPR and data protection
  • Boiler