Example 8: Example 8: The domain of the function f(x) log2 sin x is a R - Maths - Sets

Question

Example 8:

Example 8: The domain of the function f(x) log2 sin x
is

a   R                
                 
                 
              b   R ~ n
π : n ∈ I   c   R ~ n π : n ∈ N  
      d   ∪ n ∈ I 2 n π , 2 n + 1
π

Shivam Mishra · Accepted Answer

Dear Student,
Please find below the solution to the asked query:

fx=log2sinxQuantity inside log must be positive, hencesinx>0We know that sinx is positve in first and second quadrant, hencex∈0,πAlso sinx repreats in interval of 2π, hencex∈∪n∈I0+2nπ,π+2nπ⇒x∈∪n∈I2nπ,2n+1π
optionD

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Example 8: Example 8: The domain of the function f(x) log2 sin x is a R b R ~ n π : n ∈ I c R ~ n π : n ∈ N d ∪ n ∈ I 2 n π , 2 n + 1 π

Example 8:

Example 8: The domain of the function f(x) log₂ sin x is

$(a) R (b) R ~ \{n π : n \in I\} (c) R ~ \{n π : n \in N\} (d) \underset{n \in I}{\cup} (2 n π, (2 n + 1) π)$