Convert to Interval Notation cos(x)<0

Problem

cos(x)<0

Solution

1. Identify the intervals on the unit circle where the cosine function is negative. Cosine represents the xcoordinate, which is negative in the second and third quadrants.

2. Determine the primary interval within one full rotation [0,2*π) The cosine function is negative when the angle x is between π/2 and (3*π)/2

3. Account for the periodicity of the cosine function. Since cos(x) repeats every 2*π radians, we add 2*π*n to the endpoints of the interval, where n is any integer.

4. Express the solution in interval notation. Because the inequality is strict (<, use parentheses to indicate that the endpoints are not included.

Final Answer

(π/2+2*π*n,(3*π)/2+2*π*n),n∈ℤ

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