Answer to Question #217194 in Analytic Geometry for evatanshinda

Question #217194

Let x be an element of 0, [0, π]. We consider the inequalities {sinx>=[(2)^1/2]/2, 0<=cosx<(1/2). Which of the following statements is correct?


A. X is an element belonging to [π/4, π/3[;

B. X is an element belonging to ]π/4, 3π/4[

C. X is an element belonging to ]π/3, π]

D. X is an element beleonging to ]π/3, π/2]


1
Expert's answer
2021-07-19T05:53:09-0400

If x[0,π],x\in[0,\pi], then


sinx22=>π4x3π4\sin x\geq\dfrac{\sqrt{2}}{2}=>\dfrac{\pi}{4}\leq x\leq \dfrac{3\pi}{4}


0cosx<12=>π3<xπ20\leq\cos x<\dfrac{1}{2}=>\dfrac{\pi}{3}< x\leq \dfrac{\pi}{2}

Then


π3<xπ2\dfrac{\pi}{3}< x\leq \dfrac{\pi}{2}

D. X is an element belonging to ]π/3, π/2]




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