Solve for x csc(x)=1

Problem

csc(x)=1

Solution

1. Rewrite the cosecant function in terms of the sine function using the reciprocal identity csc(x)=1/sin(x)

1/sin(x)=1

2. Solve for sin(x) by taking the reciprocal of both sides of the equation.

sin(x)=1

3. Identify the values of x on the unit circle where the ycoordinate is equal to 1

x=π/2

4. Generalize the solution to include all possible angles by adding integer multiples of the period 2*π where n is any integer.

x=π/2+2*n*π

Final Answer

csc(x)=1⇒x=π/2+2*n*π

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