Answer to Question #217194 in Analytic Geometry for evatanshinda

Question

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]

Answer 1

If $x\in[0,\pi],$ then

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

$$0\leq\cos x<\dfrac{1}{2}=>\dfrac{\pi}{3}< x\leq \dfrac{\pi}{2}$$

Then

$$\dfrac{\pi}{3}< x\leq \dfrac{\pi}{2}$$

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