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tmua.me Medium Set D Paper 2 · Q13

Paper 2TrigonometryFunctions & graphs

What is the total length of the parts of the range 0≤θ<2π0\leq\theta<2\pi for which both

2sin⁡2θ<1+cos⁡θand2cos⁡2θ>1+sin⁡θ2\sin^2\theta<1+\cos\theta \qquad\text{and}\qquad 2\cos^2\theta>1+\sin\theta

hold?

Aπ3\dfrac{\pi}{3}
B4π3\dfrac{4\pi}{3}
Cπ6\dfrac{\pi}{6}
D2π3\dfrac{2\pi}{3}
E3π2\dfrac{3\pi}{2}
Fπ2\dfrac{\pi}{2}

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