Solve for x csc(x)=-1

Problem

csc(x)=−1

Solution

1. Rewrite the equation 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.

sin(x)=−1

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

x=(3*π)/2

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

x=(3*π)/2+2*π*n

Final Answer

csc(x)=−1⇒x=(3*π)/2+2*π*n

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