The value of ordinate of the graph of y = 2 - sin x lies in the interval

  1. [1, 3]
  2. [0, 3]
  3. [-1, 1]
  4. None of these

Answer (Detailed Solution Below)

Option 1 : [1, 3]
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Detailed Solution

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Concept:

The cartesian coordinate obtained by measuring parallel to the y-axis. 

Calculation:

Given: y = 2 - sin x  

The function sin x has all real numbers in its domain, but Range is -1 ≤ sin x ≤ 1 or  -1 ≤ -sin x ≤ 1

 -1 ≤ -sin x ≤ 1

Adding 2 both sides, we get

⇒ 2 - 1 ≤ 2 - sin x ≤ 2 + 1

⇒ 1 ≤ y ≤ 3

y ∈ [ 1 , 3 ] 

The correct option is 1.

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