Solve for x cos(x)<0

Problem

cos(x)<0

Solution

1. Identify the quadrants on the unit circle where the xcoordinate (representing the cosine function) is negative.

2. Determine the boundary angles where cos(x)=0 which occur at x=π/2 and x=(3*π)/2 within the interval [0,2*π)

3. Observe that the cosine function is negative in the second and third quadrants, specifically between the angles π/2 and (3*π)/2

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

Final Answer

π/2+2*n*π<x<(3*π)/2+2*n*π,n∈ℤ

Want more problems? Check here!