Solve for x csc(x)+1=0

Problem

csc(x)+1=0

Solution

1. Isolate the cosecant function by subtracting 1 from both sides of the equation.

csc(x)=−1

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

1/sin(x)=−1

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

sin(x)=−1

4. Identify the angles on the unit circle where the y-coordinate is −1

x=(3*π)/2

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

x=(3*π)/2+2*π*n

Final Answer

csc(x)+1=0⇒x=(3*π)/2+2*π*n

Want more problems? Check here!