If x,y∈[-1,0] and [ ] represents the greatest integer function then find the possible values of [cos-1x] + [cot-1y].
Answers
Given : x,y∈[-1,0] and [ ] represents the greatest integer function
Step-by-step explanation:
x,y∈[-1,0] and [ ] represents the greatest integer function
=> possible Values of x & y are between - 1 & 0
principal value of cos -¹ lies between [0 , π ] , Cos Range = [ - 1 , 1 ]
Cos⁻¹ [ - 1 , 0 ] lies between [π/2 , π ]
Cos⁻¹(0) = π/2 = 1.57 [1.57] = 1
Cos⁻¹(-1) = π = 3.14 [3.14] = 3
[Cos⁻¹(x)] = 1 , 2 , 3
principal value of cot -¹ lies between [0 , π ]
Cos⁻¹ [ - 1 , 0 ] lies between [π/2 , 3π/4 ]
Cot⁻¹(0) = π/2 = 1.57 [1.57] = 1
Cot⁻¹(-1) = 3π /4 = 2.36 [2.36] = 2
[Cot⁻¹(y)] = 1 , 2
[Cos⁻¹(x)] + [Cot⁻¹ (y)]
1 + 1 = 2
1 + 2 = 3
2 + 1 = 3
2 + 2 = 4
3 + 1 = 4
3 + 2 = 5
possible values of [Cos⁻¹(x)] + [Cot⁻¹ (y)] = 2 , 3 , 4 , 5
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