Solve for x sin(x)>0
Problem
Solution
Identify the behavior of the sine function on the unit circle. The value of
sin(x) represents they coordinate of a point on the unit circle at anglex Determine the quadrants where the
y coordinate is positive. This occurs in the first quadrant (0<x<π/2 and the second quadrant (π/2<x<π .Define the primary interval for one full rotation. The sine function is positive when
0<x<π Account for the periodicity of the sine function. Since
sin(x) has a period of2*π the inequality holds for any integerk by adding2*k*π to the boundaries.
Final Answer
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