Capítulo VII · Neste capítulo você vai
Equations
- reduce a trigonometric equation to one of the three fundamental equations;
- resolve $\operatorname{sen}\alpha = \operatorname{sen}\beta$, $\cos\alpha = \cos\beta$ and $\operatorname{tg}\alpha = \operatorname{tg}\beta$ into $\mathbb{R}$;
- select the solutions that are in a given interval;
- solve the classical equations $a\operatorname{sen} x + b\cos x = c$, sums of sines and cosines equal to zero and equations with $\operatorname{sen}^4 x + \cos^4 x$ and $\operatorname{sen}^6 x + \cos^6 x$;
- define and use the inverse circular functions $\operatorname{arc\,sen}$, $\operatorname{arc\,cos}$ and $\operatorname{arc\,tg}$.
An equation like $\operatorname{sen} x = \frac{1}{2}$ does not have just one solution: it has infinitely many, because the sine is periodic. Solving a trigonometric equation is describing all of these solutions at once, with a formula that depends on an integer $k$. To do this, it is enough to know when two arcs have the same sine, the same cosine or the same tangent — and the trigonometric cycle answers this.