FANDOM


A trigonometria é uma maneira interessante de relacionarmos lados e ângulos.

$ {\displaystyle \operatorname {sen} \,\theta ={\frac {\text{Cateto Oposto}}{\text{Hipotenusa}}}} $

$ \cos \theta = \frac{\text{Cateto adjacente}}{\text{Hipotenusa}} $

$ {\displaystyle \operatorname {tg} \theta ={\frac {\text{Cateto Oposto}}{\text{Cateto Adjacente}}}} $

PropriedadesEditar

(i) $ \operatorname{sen}(90^{\circ}-\theta)=\cos \theta $

(ii) $ \cos(90^{\circ}-\theta)=\operatorname{sen} \theta $

(iii) $ \operatorname{tg}\theta =\frac{\operatorname{sen}\theta}{\cos \theta} $

(iv) $ -1 \leq \operatorname {sen} \,\theta \leq 1 $

(v) $ -1 \leq \cos \,\theta \leq 1 $

(vi) $ \operatorname{sen} \,(2\theta) =2\operatorname{sen}\,\theta \cos \, \theta $

(vii) $ \cos \,(2\theta) =\cos^2 \, \theta-\operatorname{sen}^2\, \theta $

(viii) $ \operatorname{sen} \alpha = \operatorname{sen} \beta \Leftrightarrow \alpha = \beta + 2k \pi \textrm{ ou } \alpha = \pi - \beta + 2k\pi $ com $ k $ inteiro.

(ix) $ \operatorname{sen}(180^{\circ}-\theta)= \operatorname{sen}\theta $

(x) $ \cos (180^{\circ}-\theta) = -\cos \theta $