Question

01. Resolva a equação 2senx = -1, sendo U = R.

02. Resolva a equação 2senx = 3, sendo U = R.

03. Qual a solução da equação 2cos²x - 9cosx = 5, sendo x pertencente ao intervalo [0, 306°].

POR FAVOR ME AJUDEM GENTE!​

Answer 1

$\Large\boxed{\begin{array}{l}\tt 1)~\sf 2sen(x)=-1\\\sf sen(x)=-\dfrac{1}{2}\\\sf x=\dfrac{7\pi}{6}+2k\pi,k\in\mathbb{Z}\\\\\sf x=\dfrac{11\pi}{6}+2k\pi,k\in\mathbb{Z}\end{array}}$

$\Large\boxed{\begin{array}{l}\tt 2)~\sf 2sen(x)=3\\\sf sen(x)=\dfrac{3}{2}\\\sf S=\bigg\{\bigg\}~pois~-1\leqslant sen(x)\leqslant1\end{array}}$

$\boxed{\begin{array}{l}\tt 3)~\sf 2cos^2(x)-9cos(x)=5\\\sf 2cos^2(x)-9cos(x)-5=0\\\sf\Delta=b^2-4ac\\\sf\Delta=(-9)^2-4\cdot2\cdot(-5)\\\sf\Delta=81+40\\\sf\Delta=121\\\sf cos(x)=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\sf cos(x)=\dfrac{-(-9)\pm\sqrt{121}}{2\cdot2}\\\\\sf cos(x)=\dfrac{9\pm11}{4}\begin{cases}\sf cos(x)=\dfrac{9+11}{4}=\dfrac{20}{4}=5\\\sf cos(x)=\dfrac{9-11}{4}=-\dfrac{2\div2}{4\div2}=-\dfrac{1}{2}\end{cases}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf cos(x)=5\\\sf S=\bigg\{\bigg\}~pois~-1\leqslant cos(x)\leqslant 1\\\sf cos(x)=-\dfrac{1}{2}\\\sf x=120^\circ~ou~x=240^\circ\\\sf S=\{120^\circ,240^\circ\}\end{array}}$