Convert to Interval Notation sin(x)<0

Problem

sin(x)<0

Solution

1. Identify the intervals on the unit circle where the sine function is negative. The sine of an angle represents the ycoordinate, which is negative in the third and fourth quadrants.

2. Determine the primary interval within one full rotation, which is (π,2*π)

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

4. Express the solution as a union of intervals using interval notation.

Final Answer

sin(x)<0⇔(⋃_n∈ℤ^)((2*n+1)*π,(2*n+2)*π)

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