O seno do ângulo α é 4/5.
- Considere o ângulo α do primeiro quadrante na figura a seguir (ou anexa) e as razões trigonométricas do triângulo retângulo, seno e cosseno.
[tex]\setlength{\unitlength}{1cm}\begin{picture}(6,5)(0,0) \thicklines % \thicklines ou \thinlines \put(0,0){\line(1,0){3}} \put(0,0){\line(3,4){3}} \put(3,0){\line(0,1){4}} \qbezier [30](0.6,0.8)(1,0.5)(1,0) \put(2.6,0.4){\line(1,0){0.4}} \put(2.6,0){\line(0,1){0.4}} \put(2.8,0.2){\circle*{0.07}} \put(1.1,0.5){$\alpha$} \put(1.4,-0.5){\sf CA (3)} \put(3.3,1.5){\sf CO} \put(.4,2.3){\large \sf {hip (5)}}\end{picture}[/tex][tex]\setlength{\unitlength}{1cm} \begin{picture}(6,5)(0,0) \thicklines % \thicklines ou \thinlines\put(0,0){\line(1,0){3}}\put(0,0){\line(3,4){3}}\put(3,0){\line(0,1){4}}\qbezier [30](0.6,0.8)(1,0.5)(1,0)\put(2.6,0.4){\line(1,0){0.4}}\put(2.6,0){\line(0,1){0.4}} \put(2.8,0.2){\circle*{0.07}}\put(1.1,0.5){$\alpha$}\put(1.4,-0.5){\sf CA (3)}\put(3.3,1.5){\sf CO}\put(.4,2.3){\large \sf {hip (5)}}\end{picture}[/tex][tex]\setlength{\unitlength}{.95cm}\begin{picture}(6,5)(0,0) \thicklines % \thicklines ou \thinlines \put(0,0){\line(1,0){3}} \put(0,0){\line(3,4){3}} \put(3,0){\line(0,1){4}} \qbezier [30](0.6,0.8)(1,0.5)(1,0) \put(2.6,0.4){\line(1,0){0.4}} \put(2.6,0){\line(0,1){0.4}} \put(2.8,0.2){\circle*{0.07}} \put(1.1,0.5){$\alpha$} \put(1.4,-0.5){\sf CA (3)} \put(3.3,1.5){\sf CO} \put(.4,2.3){\large \sf {hip (5)}}\end{picture}[/tex][tex]\large \text {$ \sf sen\ \alpha = \dfrac{cateto \ oposto}{hipotenusa} $}[/tex]
[tex]\large \text {$ \sf cos\ \alpha = \dfrac{cateto \ adjacente }{hipotenusa} $}[/tex]
[tex]\setlength{\unitlength}{1cm}\begin{picture}(6,5)(0,0)\thicklines\put(0,0){\line(1,0){3}}\put(0,0){\line(3,4){3}}\put(3,0){\line(0,1){4}}\qbezier [30](0.6,0.8)(1,0.5)(1,0)\put(2.6,0.4){\line(1,0){0.4}}\put(2.6,0){\line(0,1){0.4}} \put(2.8,0.2){\circle*{0.07}}\put(1.1,0.5){$\alpha$}\put(1.4,-0.5){\sf CA (3)}\put(3.3,1.5){\sf CO}\put(.4,2.3){\large \sf {hip (5)}}\end{picture}[/tex][tex]\setlength{\unitlength}{1cm}\begin{picture}(6,5)(0,0) \thicklines % \thicklines ou \thinlines \put(0,0){\line(1,0){3}} \put(0,0){\line(3,4){3}} \put(3,0){\line(0,1){4}} \qbezier [30](0.6,0.8)(1,0.4)(1,0) \put(2.6,0.4){\line(1,0){0.4}} \put(2.6,0){\line(0,1){0.4}} \put(2.8,0.2){\circle*{0.07}} \put(1.1,0.5){$\alpha$} \put(1.4,-0.5){\sf CA (3)} \put(3.3,1.5){\sf CO} \put(.4,2.3){\large \sf {hip (5)}}\end{picture}[/tex][tex]\setlength{\unitlength}{1cm}\begin{picture}(6,5)(0,0) \thicklines % \thicklines ou \thinlines \put(0,0){\line(1,0){3}} \put(0,0){\line(3,4){3}} \put(3,0){\line(0,1){4}} \qbezier [30](0.6,0.8)(1,0.5)(1,0) \put(2.6,0.4){\line(1,0){0.4}} \put(2.6,0){\line(0,1){0.4}} \put(2.8,0.2){\circle*{0.07}} \put(1.1,0.5){$\alpha$} \put(1.4,-0.5){\sf CA (3)} \put(3.3,1.5){\sf CO} \put(.4,2.3){\large \sf {hip (5)}}\end{picture}[/tex]
- Se o cosseno do ângulo α é 3/5, então o cateto adjacente a α mede 3 unidades e a hipotenusa mede 5 unidades.
- Determine a medida do cateto oposto a α usando o teorema de Pitágoras.
hip² = CO² + CA²
5² = CO² + 3²
25 = CO² + 9
CO² = 25 − 9
CO² = 16
CO = 4
- Determine o valor do seno do ângulo α.
[tex]\large \text {$ \sf sen\ \alpha = \dfrac{CO}{hip}$}[/tex]
[tex]\boxed {\large \text {$ \sf sen\ \alpha =\dfrac {4}{5}$}}[/tex]
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