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If A = {x : cosx > - 1/2 and 0 ≤ x ≤ π} , B = {x : sinx > 1/2 and π/3 ≤ x ≤ π} Then A ∩ B = (A) [π, 5π/6) (B) [π, 7π/6) (C) [π/3, 2π/3) (D) [0, 5π/6) The given answer is: (C) [π/3, 2π/3) but shouldn't it be [ π/6, 2π/3) ????? Please help......


  If  A = {x : cosx > - 1/2 and 0 ≤ x ≤ π} ,  B = {x : sinx > 1/2 and π/3 ≤ x ≤ π}


         Then A ∩ B =


(A)    [π, 5π/6)                                                                 


(B)    [π, 7π/6) 


(C)    [π/3, 2π/3)                                                               


(D)    [0, 5π/6)   


The given answer is:


(C)    [π/3, 2π/3) 


but shouldn't it be [π/6, 2π/3) ?????


Please help......

Grade:10

1 Answers

Chetan Mandayam Nayakar
312 Points
9 years ago

cosx>-1/2,leads to A=[0,2π/3)

sinx>1/2 leads to B=(π/6,5π/6)

A∩B = (π/6,2π/3)

The solution in the book is wrong as you suspect.

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