Find the Domain y=csc(x)

Problem

y=csc(x)

Solution

1. Identify the definition of the cosecant function in terms of sine.

csc(x)=1/sin(x)

2. Determine the condition for the domain by identifying where the function is undefined. A fraction is undefined when the denominator is equal to zero.

sin(x)=0

3. Solve the equation for x to find the values that must be excluded from the domain. The sine function is zero at all integer multiples of π

x=n*π

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

x≠n*π

Final Answer

Domain:{x|x∈ℝ,x≠n*π,n∈ℤ}

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