Solve for x sin(x)=-1

Problem

sin(x)=−1

Solution

1. Identify the values on the unit circle where the sine function, which represents the y-coordinate, is equal to −1

2. Locate the angle within one full rotation [0,2*π) The sine value is −1 only at the bottom of the unit circle.

3. Determine the specific angle in radians. At the bottom of the circle, the angle is (3*π)/2

4. Generalize the solution to account for the periodicity of the sine function. Since sine repeats every 2*π radians, add 2*π*n to the result, where n is any integer.

Final Answer

x=(3*π)/2+2*π*n

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