Capítulo VIII · Neste capítulo você vai

Inequalities

  • recognize the six fundamental inequalities: $\operatorname{sen} x$, $\cos x$ or $\operatorname{tg} x$ greater or less than a number $m$;
  • resolve them by marking the appropriate arc in the cycle and describing it at intervals;
  • reduce other inequalities to fundamental ones, by factoring, changing variables or sign chart;
  • select solutions that are in a given range.

A trigonometric equation marks points in the cycle; an inequality marks arcos. Solving $\operatorname{sen} x > \frac{1}{2}$ is finding the part of the cycle that is above the straight line $v = \frac{1}{2}$ and translating this arc into intervals — taking care to go through the cycle starting from $A$, in a counterclockwise direction.

Choose the function, the direction of the inequality and the value of $m$: the red arc of the cycle and the red band of the $x$ axis are the solutions in $[0, 2\pi]$.