Find the Domain csc(x)=1/(sin(x))

Problem

csc(x)=1/sin(x)

Solution

1. Identify the condition for the domain of a rational function. The function is undefined where the denominator is equal to zero.

2. Set the denominator equal to zero to find the excluded values.

sin(x)=0

3. Solve for x using the properties of the sine function. The sine function is zero at all integer multiples of π

x=n*π

4. Define the domain by excluding these values from the set of all real numbers, where n is any integer.

{[x∈ℝ,x≠n*π,n∈ℤ]}

Final Answer

Domain of *csc(x)={[x∈ℝ,x≠n*π,n∈ℤ]}

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