Bonjour,
Si α ∈ ]π ; 3π/2[, alors sin α < 0 , cos α < 0 et tan α >0.
[tex]cos^2\alpha+sin^2\alpha=1\\\\cos^2\alpha=1-sin^2\alpha\\\\cos^2\alpha=1-(-\dfrac{3}{5})^2\\\\cos^2\alpha=1-\dfrac{9}{25}\\\\cos^2\alpha=\dfrac{25}{25}-\dfrac{9}{25}\\\\cos^2\alpha=\dfrac{16}{25}\\\\cos\ \alpha=-\dfrac{4}{5}\ \ ou\ \ cos\ \alpha=\dfrac{4}{5}[/tex]
or cos α < 0.
Donc [tex]cos\alpha=-\dfrac{4}{5}[/tex]
[tex]tan\ \alpha=\dfrac{sin\ \alpha}{cos\ \alpha}\\\\\\tan\ \alpha=\dfrac{-\dfrac{3}{5}}{-\dfrac{4}{5}}\\\\\\tan\ \alpha=-\dfrac{3}{5}\times(-\dfrac{5}{4})\\\\\\tan\ \alpha=\dfrac{3}{4}[/tex]
